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Integrability of Nonlinear Systems [[electronic resource] /] / edited by Yvette Kosmann-Schwarzbach, Basil Grammaticos, Kilkothur M. Tamizhmani
| Integrability of Nonlinear Systems [[electronic resource] /] / edited by Yvette Kosmann-Schwarzbach, Basil Grammaticos, Kilkothur M. Tamizhmani |
| Edizione | [1st ed. 1997.] |
| Pubbl/distr/stampa | Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 1997 |
| Descrizione fisica | 1 online resource (VII, 380 p.) |
| Disciplina | 515/.355 |
| Collana | Lecture Notes in Physics |
| Soggetto topico |
Mathematical physics
Fluids Mechanics Theoretical, Mathematical and Computational Physics Fluid- and Aerodynamics Classical Mechanics |
| ISBN | 3-540-69521-4 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Nonlinear waves, solitons and IST -- Integrability — and how to detect it -- to the Hirota bilinear method -- Lie bialgebras, poisson Lie groups and dressing transformations -- Analytic and asymptotic methods for nonlinear singularity analysis: a review and extensions of tests for the Painlevé property -- Bifurcations, chaos, controlling and synchronization of certain nonlinear oscillators -- Eight lectures on integrable systems -- Bilinear formalism in solition theory -- Quantum and classical integrable systems. |
| Record Nr. | UNISA-996466795703316 |
| Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 1997 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Integrability of Nonlinear Systems [[electronic resource] /] / edited by Yvette Kosmann-Schwarzbach, Basil Grammaticos, Kilkothur M. Tamizhmani
| Integrability of Nonlinear Systems [[electronic resource] /] / edited by Yvette Kosmann-Schwarzbach, Basil Grammaticos, Kilkothur M. Tamizhmani |
| Edizione | [1st ed. 1997.] |
| Pubbl/distr/stampa | Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 1997 |
| Descrizione fisica | 1 online resource (VII, 380 p.) |
| Disciplina | 515/.355 |
| Collana | Lecture Notes in Physics |
| Soggetto topico |
Mathematical physics
Fluids Mechanics Theoretical, Mathematical and Computational Physics Fluid- and Aerodynamics Classical Mechanics |
| ISBN | 3-540-69521-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Nonlinear waves, solitons and IST -- Integrability — and how to detect it -- to the Hirota bilinear method -- Lie bialgebras, poisson Lie groups and dressing transformations -- Analytic and asymptotic methods for nonlinear singularity analysis: a review and extensions of tests for the Painlevé property -- Bifurcations, chaos, controlling and synchronization of certain nonlinear oscillators -- Eight lectures on integrable systems -- Bilinear formalism in solition theory -- Quantum and classical integrable systems. |
| Record Nr. | UNINA-9910257385303321 |
| Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 1997 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Mathematical aspects of nonlinear dispersive equations [[electronic resource] /] / Jean Bourgain, Carlos E. Kenig, and S. Klainerman, editors
| Mathematical aspects of nonlinear dispersive equations [[electronic resource] /] / Jean Bourgain, Carlos E. Kenig, and S. Klainerman, editors |
| Edizione | [Course Book] |
| Pubbl/distr/stampa | Princeton, : Princeton University Press, 2007 |
| Descrizione fisica | 1 online resource (309 p.) |
| Disciplina | 515/.355 |
| Altri autori (Persone) |
BourgainJean <1954->
KenigCarlos E. <1953-> KlainermanSergiu <1950-> |
| Collana | Annals of mathematics studies |
| Soggetto topico |
Differential equations, Nonlinear
Nonlinear partial differential operators |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-282-12960-0
9786612129605 1-4008-2779-5 |
| Classificazione | SI 830 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Frontmatter -- Contents -- Preface -- Chapter 1. On Strichartz's Inequalities and the Nonlinear Schrödinger Equation on Irrational Tori / Bourgain, J. -- Chapter 2. Diffusion Bound for a Nonlinear Schrödinger Equation / Bourgain, J. / Wang, W.-M. -- Chapter 3. Instability of Finite Difference Schemes for Hyperbolic Conservation Laws / Bressan, A. / Baiti, P. / Jenssen, H. K. -- Chapter 4. Nonlinear Elliptic Equations with Measures Revisited / Brezis, H. / Marcus, M. / Ponce, A. C. -- Chapter 5. Global Solutions for the Nonlinear Schrödinger Equation on Three-Dimensional Compact Manifolds / Burq, N. / Gérard, P. / Tzvetkov, N. -- Chapter 6. Power Series Solution of a Nonlinear Schrödinger Equation / Christ, M. -- Chapter 7. Eulerian-Lagrangian Formalism and Vortex Reconnection / Constantin, P. -- Chapter 8. Long Time Existence for Small Data Semilinear Klein-Gordon Equations on Spheres / Delort, J.-M. / Szeftel, J. -- Chapter 9. Local and Global Wellposedness of Periodic KP-I Equations / Ionescu, A. D. / Kenig, C. E. -- Chapter 10. The Cauchy Problem for the Navier-Stokes Equations with Spatially Almost Periodic Initial Data / Giga, Y. / Mahalov, A. / Nicolaenko, B. -- Chapter 11. Longtime Decay Estimates for the Schrödinger Equation on Manifolds / Rodnianski, I. / Tao, T. -- Contributors -- Index |
| Record Nr. | UNINA-9910454344603321 |
| Princeton, : Princeton University Press, 2007 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Mathematical aspects of nonlinear dispersive equations [[electronic resource] /] / Jean Bourgain, Carlos E. Kenig, and S. Klainerman, editors
| Mathematical aspects of nonlinear dispersive equations [[electronic resource] /] / Jean Bourgain, Carlos E. Kenig, and S. Klainerman, editors |
| Edizione | [Course Book] |
| Pubbl/distr/stampa | Princeton, : Princeton University Press, 2007 |
| Descrizione fisica | 1 online resource (309 p.) |
| Disciplina | 515/.355 |
| Altri autori (Persone) |
BourgainJean <1954->
KenigCarlos E. <1953-> KlainermanSergiu <1950-> |
| Collana | Annals of mathematics studies |
| Soggetto topico |
Differential equations, Nonlinear
Nonlinear partial differential operators |
| Soggetto non controllato |
Absolute value
Addition Analysis Analytical technique Average Commutator Conservation law Continuous spectrum Critical focus Eigenfunction Eigenvalues and eigenvectors Equation Exponential decay Fourier transform Lecture Manifold Medium frequency Nature Navier–Stokes equations Nonlinear system Scattering theory Sloan Fellowship Spectral method Subset Support (mathematics) Theory Three-dimensional space (mathematics) Volume Wave equation |
| ISBN |
1-282-12960-0
9786612129605 1-4008-2779-5 |
| Classificazione | SI 830 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Frontmatter -- Contents -- Preface -- Chapter 1. On Strichartz's Inequalities and the Nonlinear Schrödinger Equation on Irrational Tori / Bourgain, J. -- Chapter 2. Diffusion Bound for a Nonlinear Schrödinger Equation / Bourgain, J. / Wang, W.-M. -- Chapter 3. Instability of Finite Difference Schemes for Hyperbolic Conservation Laws / Bressan, A. / Baiti, P. / Jenssen, H. K. -- Chapter 4. Nonlinear Elliptic Equations with Measures Revisited / Brezis, H. / Marcus, M. / Ponce, A. C. -- Chapter 5. Global Solutions for the Nonlinear Schrödinger Equation on Three-Dimensional Compact Manifolds / Burq, N. / Gérard, P. / Tzvetkov, N. -- Chapter 6. Power Series Solution of a Nonlinear Schrödinger Equation / Christ, M. -- Chapter 7. Eulerian-Lagrangian Formalism and Vortex Reconnection / Constantin, P. -- Chapter 8. Long Time Existence for Small Data Semilinear Klein-Gordon Equations on Spheres / Delort, J.-M. / Szeftel, J. -- Chapter 9. Local and Global Wellposedness of Periodic KP-I Equations / Ionescu, A. D. / Kenig, C. E. -- Chapter 10. The Cauchy Problem for the Navier-Stokes Equations with Spatially Almost Periodic Initial Data / Giga, Y. / Mahalov, A. / Nicolaenko, B. -- Chapter 11. Longtime Decay Estimates for the Schrödinger Equation on Manifolds / Rodnianski, I. / Tao, T. -- Contributors -- Index |
| Record Nr. | UNINA-9910777728603321 |
| Princeton, : Princeton University Press, 2007 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Mathematical aspects of nonlinear dispersive equations / / Jean Bourgain, Carlos E. Kenig, and S. Klainerman, editors
| Mathematical aspects of nonlinear dispersive equations / / Jean Bourgain, Carlos E. Kenig, and S. Klainerman, editors |
| Edizione | [Course Book] |
| Pubbl/distr/stampa | Princeton, : Princeton University Press, 2007 |
| Descrizione fisica | 1 online resource (309 p.) |
| Disciplina | 515/.355 |
| Altri autori (Persone) |
BourgainJean <1954->
KenigCarlos E. <1953-> KlainermanSergiu <1950-> |
| Collana | Annals of mathematics studies |
| Soggetto topico |
Differential equations, Nonlinear
Nonlinear partial differential operators |
| ISBN |
1-282-12960-0
9786612129605 1-4008-2779-5 |
| Classificazione | SI 830 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Frontmatter -- Contents -- Preface -- Chapter 1. On Strichartz's Inequalities and the Nonlinear Schrödinger Equation on Irrational Tori / Bourgain, J. -- Chapter 2. Diffusion Bound for a Nonlinear Schrödinger Equation / Bourgain, J. / Wang, W.-M. -- Chapter 3. Instability of Finite Difference Schemes for Hyperbolic Conservation Laws / Bressan, A. / Baiti, P. / Jenssen, H. K. -- Chapter 4. Nonlinear Elliptic Equations with Measures Revisited / Brezis, H. / Marcus, M. / Ponce, A. C. -- Chapter 5. Global Solutions for the Nonlinear Schrödinger Equation on Three-Dimensional Compact Manifolds / Burq, N. / Gérard, P. / Tzvetkov, N. -- Chapter 6. Power Series Solution of a Nonlinear Schrödinger Equation / Christ, M. -- Chapter 7. Eulerian-Lagrangian Formalism and Vortex Reconnection / Constantin, P. -- Chapter 8. Long Time Existence for Small Data Semilinear Klein-Gordon Equations on Spheres / Delort, J.-M. / Szeftel, J. -- Chapter 9. Local and Global Wellposedness of Periodic KP-I Equations / Ionescu, A. D. / Kenig, C. E. -- Chapter 10. The Cauchy Problem for the Navier-Stokes Equations with Spatially Almost Periodic Initial Data / Giga, Y. / Mahalov, A. / Nicolaenko, B. -- Chapter 11. Longtime Decay Estimates for the Schrödinger Equation on Manifolds / Rodnianski, I. / Tao, T. -- Contributors -- Index |
| Record Nr. | UNINA-9910813829203321 |
| Princeton, : Princeton University Press, 2007 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Nonlinear behavior and stability of thin-walled shells / / Natalia I. Obodan, Olexandr G. Lebedeyev, Vasilii A. Gromov
| Nonlinear behavior and stability of thin-walled shells / / Natalia I. Obodan, Olexandr G. Lebedeyev, Vasilii A. Gromov |
| Autore | Obodan Natalia I |
| Edizione | [1st ed. 2013.] |
| Pubbl/distr/stampa | Dordrecht, : Springer, c2013 |
| Descrizione fisica | 1 online resource (182 p.) |
| Disciplina |
515.355
515/.355 |
| Altri autori (Persone) |
LebedeyevOlexandr G
GromovVasilii A. |
| Collana | Solid Mechanics and Its Applications |
| Soggetto topico |
Thin-walled structures
Shells (Engineering) |
| ISBN | 94-007-6365-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 1. In lieu of introduction -- 2. Boundary problem of thin shells theory -- 3. Branching of nonlinear boundary problem solutions -- 4. Numerical method -- 5. Nonaxisymmetrically loaded cylindrical shell -- 6. Structurally nonaxisymetric shell subjected to uniform loading -- 7. Postcritical branching patterns for cylindrical shell subjected to uniform external loading -- 8. Postbuckling behaviour and stability of anisotropic shells -- 9. Conclusion. |
| Record Nr. | UNINA-9910438052503321 |
Obodan Natalia I
|
||
| Dordrecht, : Springer, c2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Nonlinear Differential Equations and Dynamical Systems [[electronic resource] /] / by Ferdinand Verhulst
| Nonlinear Differential Equations and Dynamical Systems [[electronic resource] /] / by Ferdinand Verhulst |
| Autore | Verhulst Ferdinand |
| Edizione | [2nd ed. 1996.] |
| Pubbl/distr/stampa | Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 1996 |
| Descrizione fisica | 1 online resource (X, 306 p. 2 illus.) |
| Disciplina | 515/.355 |
| Collana | Universitext |
| Soggetto topico |
Mathematical analysis
Analysis (Mathematics) Dynamics Ergodic theory Physics Statistical physics Dynamical systems Applied mathematics Engineering mathematics Analysis Dynamical Systems and Ergodic Theory Numerical and Computational Physics, Simulation Complex Systems Mathematical and Computational Engineering Statistical Physics and Dynamical Systems |
| ISBN | 3-642-61453-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 1 Introduction -- 1.1 Definitions and notation -- 1.2 Existence and uniqueness -- 1.3 Gronwall’s inequality -- 2 Autonomous equations -- 2.1 Phase-space, orbits -- 2.2 Critical points and linearisation -- 2.3 Periodic solutions -- 2.4 First integrals and integral manifolds -- 2.5 Evolution of a volume element, Liouville’s theorem -- 2.6 Exercises -- 3 Critical points -- 3.1 Two-dimensional linear systems -- 3.2 Remarks on three-dimensional linear systems -- 3.3 Critical points of nonlinear equations -- 3.4 Exercises -- 4 Periodic solutions -- 4.1 Bendixson’s criterion -- 4.2 Geometric auxiliaries, preparation for the Poincaré-Bendixson theorem -- 4.3 The Poincaré-Bendixson theorem -- 4.4 Applications of the Poincaré-Bendixson theorem -- 4.5 Periodic solutions in ?n -- 4.6 Exercises -- 5 Introduction to the theory of stability -- 5.1 Simple examples -- 5.2 Stability of equilibrium solutions -- 5.3 Stability of periodic solutions -- 5.4 Linearisation -- 5.5 Exercises -- 6 Linear Equations -- 6.1 Equations with constant coefficients -- 6.2 Equations with coefficients which have a limit -- 6.3 Equations with periodic coefficients -- 6.4 Exercises -- 7 Stability by linearisation -- 7.1 Asymptotic stability of the trivial solution -- 7.2 Instability of the trivial solution -- 7.3 Stability of periodic solutions of autonomous equations -- 7.4 Exercises -- 8 Stability analysis by the direct method -- 8.1 Introduction -- 8.2 Lyapunov functions -- 8.3 Hamiltonian systems and systems with first integrals -- 8.4 Applications and examples -- 8.5 Exercises -- 9 Introduction to perturbation theory -- 9.1 Background and elementary examples -- 9.2 Basic material -- 9.3 Naïve expansion -- 9.4 The Poincaré expansion theorem -- 9.5 Exercises -- 10 The Poincaré-Lindstedt method -- 10.1 Periodic solutions of autonomous second-order equations -- 10.2 Approximation of periodic solutions on arbitrary long time-scales -- 10.3 Periodic solutions of equations with forcing terms -- 10.4 The existence of periodic solutions -- 10.5 Exercises -- 11 The method of averaging -- 11.1 Introduction -- 11.2 The Lagrange standard form -- 11.3 Averaging in the periodic case -- 11.4 Averaging in the general case -- 11.5 Adiabatic invariants -- 11.6 Averaging over one angle, resonance manifolds -- 11.7 Averaging over more than one angle, an introduction -- 11.8 Periodic solutions -- 11.9 Exercises -- 12 Relaxation Oscillations -- 12.1 Introduction -- 12.2 Mechanical systems with large friction -- 12.3 The van der Pol-equation -- 12.4 The Volterra-Lotka equations -- 12.5 Exercises -- 13 Bifurcation Theory -- 13.1 Introduction -- 13.2 Normalisation -- 13.3 Averaging and normalisation -- 13.4 Centre manifolds -- 13.5 Bifurcation of equilibrium solutions and Hopf bifurcation -- 13.6 Exercises -- 14 Chaos -- 14.1 Introduction and historical context -- 14.2 The Lorenz-equations -- 14.3 Maps associated with the Lorenz-equations -- 14.4 One-dimensional dynamics -- 14.5 One-dimensional chaos: the quadratic map -- 14.6 One-dimensional chaos: the tent map -- 14.7 Fractal sets -- 14.8 Dynamical characterisations of fractal sets -- 14.9 Lyapunov exponents -- 14.10 Ideas and references to the literature -- 15 Hamiltonian systems -- 15.1 Introduction -- 15.2 A nonlinear example with two degrees of freedom -- 15.3 Birkhoff-normalisation -- 15.4 The phenomenon of recurrence -- 15.5 Periodic solutions -- 15.6 Invariant tori and chaos -- 15.7 The KAM theorem -- 15.8 Exercises -- Appendix 1: The Morse lemma -- Appendix 2: Linear periodic equations with a small parameter -- Appendix 3: Trigonometric formulas and averages -- Appendix 4: A sketch of Cotton’s proof of the stable and unstable manifold theorem 3.3 -- Appendix 5: Bifurcations of self-excited oscillations -- Appendix 6: Normal forms of Hamiltonian systems near equilibria -- Answers and hints to the exercises -- References. |
| Record Nr. | UNINA-9910480045903321 |
|
Verhulst Ferdinand
|
||
| Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 1996 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Nonlinear Differential Equations and Dynamical Systems [[electronic resource] /] / by Ferdinand Verhulst
| Nonlinear Differential Equations and Dynamical Systems [[electronic resource] /] / by Ferdinand Verhulst |
| Autore | Verhulst Ferdinand |
| Edizione | [2nd ed. 1996.] |
| Pubbl/distr/stampa | Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 1996 |
| Descrizione fisica | 1 online resource (X, 306 p. 2 illus.) |
| Disciplina | 515/.355 |
| Collana | Universitext |
| Soggetto topico |
Mathematical analysis
Analysis (Mathematics) Dynamics Ergodic theory Physics Statistical physics Dynamical systems Applied mathematics Engineering mathematics Analysis Dynamical Systems and Ergodic Theory Numerical and Computational Physics, Simulation Complex Systems Mathematical and Computational Engineering Statistical Physics and Dynamical Systems |
| ISBN | 3-642-61453-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 1 Introduction -- 1.1 Definitions and notation -- 1.2 Existence and uniqueness -- 1.3 Gronwall’s inequality -- 2 Autonomous equations -- 2.1 Phase-space, orbits -- 2.2 Critical points and linearisation -- 2.3 Periodic solutions -- 2.4 First integrals and integral manifolds -- 2.5 Evolution of a volume element, Liouville’s theorem -- 2.6 Exercises -- 3 Critical points -- 3.1 Two-dimensional linear systems -- 3.2 Remarks on three-dimensional linear systems -- 3.3 Critical points of nonlinear equations -- 3.4 Exercises -- 4 Periodic solutions -- 4.1 Bendixson’s criterion -- 4.2 Geometric auxiliaries, preparation for the Poincaré-Bendixson theorem -- 4.3 The Poincaré-Bendixson theorem -- 4.4 Applications of the Poincaré-Bendixson theorem -- 4.5 Periodic solutions in ?n -- 4.6 Exercises -- 5 Introduction to the theory of stability -- 5.1 Simple examples -- 5.2 Stability of equilibrium solutions -- 5.3 Stability of periodic solutions -- 5.4 Linearisation -- 5.5 Exercises -- 6 Linear Equations -- 6.1 Equations with constant coefficients -- 6.2 Equations with coefficients which have a limit -- 6.3 Equations with periodic coefficients -- 6.4 Exercises -- 7 Stability by linearisation -- 7.1 Asymptotic stability of the trivial solution -- 7.2 Instability of the trivial solution -- 7.3 Stability of periodic solutions of autonomous equations -- 7.4 Exercises -- 8 Stability analysis by the direct method -- 8.1 Introduction -- 8.2 Lyapunov functions -- 8.3 Hamiltonian systems and systems with first integrals -- 8.4 Applications and examples -- 8.5 Exercises -- 9 Introduction to perturbation theory -- 9.1 Background and elementary examples -- 9.2 Basic material -- 9.3 Naïve expansion -- 9.4 The Poincaré expansion theorem -- 9.5 Exercises -- 10 The Poincaré-Lindstedt method -- 10.1 Periodic solutions of autonomous second-order equations -- 10.2 Approximation of periodic solutions on arbitrary long time-scales -- 10.3 Periodic solutions of equations with forcing terms -- 10.4 The existence of periodic solutions -- 10.5 Exercises -- 11 The method of averaging -- 11.1 Introduction -- 11.2 The Lagrange standard form -- 11.3 Averaging in the periodic case -- 11.4 Averaging in the general case -- 11.5 Adiabatic invariants -- 11.6 Averaging over one angle, resonance manifolds -- 11.7 Averaging over more than one angle, an introduction -- 11.8 Periodic solutions -- 11.9 Exercises -- 12 Relaxation Oscillations -- 12.1 Introduction -- 12.2 Mechanical systems with large friction -- 12.3 The van der Pol-equation -- 12.4 The Volterra-Lotka equations -- 12.5 Exercises -- 13 Bifurcation Theory -- 13.1 Introduction -- 13.2 Normalisation -- 13.3 Averaging and normalisation -- 13.4 Centre manifolds -- 13.5 Bifurcation of equilibrium solutions and Hopf bifurcation -- 13.6 Exercises -- 14 Chaos -- 14.1 Introduction and historical context -- 14.2 The Lorenz-equations -- 14.3 Maps associated with the Lorenz-equations -- 14.4 One-dimensional dynamics -- 14.5 One-dimensional chaos: the quadratic map -- 14.6 One-dimensional chaos: the tent map -- 14.7 Fractal sets -- 14.8 Dynamical characterisations of fractal sets -- 14.9 Lyapunov exponents -- 14.10 Ideas and references to the literature -- 15 Hamiltonian systems -- 15.1 Introduction -- 15.2 A nonlinear example with two degrees of freedom -- 15.3 Birkhoff-normalisation -- 15.4 The phenomenon of recurrence -- 15.5 Periodic solutions -- 15.6 Invariant tori and chaos -- 15.7 The KAM theorem -- 15.8 Exercises -- Appendix 1: The Morse lemma -- Appendix 2: Linear periodic equations with a small parameter -- Appendix 3: Trigonometric formulas and averages -- Appendix 4: A sketch of Cotton’s proof of the stable and unstable manifold theorem 3.3 -- Appendix 5: Bifurcations of self-excited oscillations -- Appendix 6: Normal forms of Hamiltonian systems near equilibria -- Answers and hints to the exercises -- References. |
| Record Nr. | UNINA-9910789217203321 |
|
Verhulst Ferdinand
|
||
| Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 1996 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Nonlinear Differential Equations and Dynamical Systems / / by Ferdinand Verhulst
| Nonlinear Differential Equations and Dynamical Systems / / by Ferdinand Verhulst |
| Autore | Verhulst Ferdinand |
| Edizione | [2nd ed. 1996.] |
| Pubbl/distr/stampa | Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 1996 |
| Descrizione fisica | 1 online resource (X, 306 p. 2 illus.) |
| Disciplina | 515/.355 |
| Collana | Universitext |
| Soggetto topico |
Mathematical analysis
Analysis (Mathematics) Dynamics Ergodic theory Physics Statistical physics Dynamical systems Applied mathematics Engineering mathematics Analysis Dynamical Systems and Ergodic Theory Numerical and Computational Physics, Simulation Complex Systems Mathematical and Computational Engineering Statistical Physics and Dynamical Systems |
| ISBN | 3-642-61453-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 1 Introduction -- 1.1 Definitions and notation -- 1.2 Existence and uniqueness -- 1.3 Gronwall’s inequality -- 2 Autonomous equations -- 2.1 Phase-space, orbits -- 2.2 Critical points and linearisation -- 2.3 Periodic solutions -- 2.4 First integrals and integral manifolds -- 2.5 Evolution of a volume element, Liouville’s theorem -- 2.6 Exercises -- 3 Critical points -- 3.1 Two-dimensional linear systems -- 3.2 Remarks on three-dimensional linear systems -- 3.3 Critical points of nonlinear equations -- 3.4 Exercises -- 4 Periodic solutions -- 4.1 Bendixson’s criterion -- 4.2 Geometric auxiliaries, preparation for the Poincaré-Bendixson theorem -- 4.3 The Poincaré-Bendixson theorem -- 4.4 Applications of the Poincaré-Bendixson theorem -- 4.5 Periodic solutions in ?n -- 4.6 Exercises -- 5 Introduction to the theory of stability -- 5.1 Simple examples -- 5.2 Stability of equilibrium solutions -- 5.3 Stability of periodic solutions -- 5.4 Linearisation -- 5.5 Exercises -- 6 Linear Equations -- 6.1 Equations with constant coefficients -- 6.2 Equations with coefficients which have a limit -- 6.3 Equations with periodic coefficients -- 6.4 Exercises -- 7 Stability by linearisation -- 7.1 Asymptotic stability of the trivial solution -- 7.2 Instability of the trivial solution -- 7.3 Stability of periodic solutions of autonomous equations -- 7.4 Exercises -- 8 Stability analysis by the direct method -- 8.1 Introduction -- 8.2 Lyapunov functions -- 8.3 Hamiltonian systems and systems with first integrals -- 8.4 Applications and examples -- 8.5 Exercises -- 9 Introduction to perturbation theory -- 9.1 Background and elementary examples -- 9.2 Basic material -- 9.3 Naïve expansion -- 9.4 The Poincaré expansion theorem -- 9.5 Exercises -- 10 The Poincaré-Lindstedt method -- 10.1 Periodic solutions of autonomous second-order equations -- 10.2 Approximation of periodic solutions on arbitrary long time-scales -- 10.3 Periodic solutions of equations with forcing terms -- 10.4 The existence of periodic solutions -- 10.5 Exercises -- 11 The method of averaging -- 11.1 Introduction -- 11.2 The Lagrange standard form -- 11.3 Averaging in the periodic case -- 11.4 Averaging in the general case -- 11.5 Adiabatic invariants -- 11.6 Averaging over one angle, resonance manifolds -- 11.7 Averaging over more than one angle, an introduction -- 11.8 Periodic solutions -- 11.9 Exercises -- 12 Relaxation Oscillations -- 12.1 Introduction -- 12.2 Mechanical systems with large friction -- 12.3 The van der Pol-equation -- 12.4 The Volterra-Lotka equations -- 12.5 Exercises -- 13 Bifurcation Theory -- 13.1 Introduction -- 13.2 Normalisation -- 13.3 Averaging and normalisation -- 13.4 Centre manifolds -- 13.5 Bifurcation of equilibrium solutions and Hopf bifurcation -- 13.6 Exercises -- 14 Chaos -- 14.1 Introduction and historical context -- 14.2 The Lorenz-equations -- 14.3 Maps associated with the Lorenz-equations -- 14.4 One-dimensional dynamics -- 14.5 One-dimensional chaos: the quadratic map -- 14.6 One-dimensional chaos: the tent map -- 14.7 Fractal sets -- 14.8 Dynamical characterisations of fractal sets -- 14.9 Lyapunov exponents -- 14.10 Ideas and references to the literature -- 15 Hamiltonian systems -- 15.1 Introduction -- 15.2 A nonlinear example with two degrees of freedom -- 15.3 Birkhoff-normalisation -- 15.4 The phenomenon of recurrence -- 15.5 Periodic solutions -- 15.6 Invariant tori and chaos -- 15.7 The KAM theorem -- 15.8 Exercises -- Appendix 1: The Morse lemma -- Appendix 2: Linear periodic equations with a small parameter -- Appendix 3: Trigonometric formulas and averages -- Appendix 4: A sketch of Cotton’s proof of the stable and unstable manifold theorem 3.3 -- Appendix 5: Bifurcations of self-excited oscillations -- Appendix 6: Normal forms of Hamiltonian systems near equilibria -- Answers and hints to the exercises -- References. |
| Record Nr. | UNINA-9910807088203321 |
|
Verhulst Ferdinand
|
||
| Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 1996 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Nonlinear partial differential equations : International Conference on Nonlinear Partial Differential Equations and Applications, March 21-24, 1998, Northwestern University / / Gui-Qiang Chen, Emmanuele DiBenedetto, editors
| Nonlinear partial differential equations : International Conference on Nonlinear Partial Differential Equations and Applications, March 21-24, 1998, Northwestern University / / Gui-Qiang Chen, Emmanuele DiBenedetto, editors |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [1999] |
| Descrizione fisica | 1 online resource (318 p.) |
| Disciplina | 515/.355 |
| Collana | Contemporary mathematics |
| Soggetto topico | Differential equations, Nonlinear |
| Soggetto genere / forma | Electronic books. |
| ISBN | 0-8218-2034-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910480753403321 |
| Providence, Rhode Island : , : American Mathematical Society, , [1999] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
