Info
Differential equations, dynamical systems, and an introduction to chaos / / Morris W. Hirsch, Stephen Smale, Robert L. Devaney [[electronic resource]]
| Differential equations, dynamical systems, and an introduction to chaos / / Morris W. Hirsch, Stephen Smale, Robert L. Devaney [[electronic resource]] |
| Autore | Hirsch Morris W. <1933-> |
| Edizione | [3rd ed.] |
| Pubbl/distr/stampa | Waltham, MA, : Academic Press, c2013 |
| Descrizione fisica | 1 online resource (xiv, 418 p. ) : ill. ; |
| Disciplina | 515/.35 |
| Altri autori (Persone) |
SmaleStephen <1930->
DevaneyRobert L. <1948-> |
| Soggetto topico |
Differential equations
Algebras, Linear Chaotic behavior in systems |
| Soggetto genere / forma | Electronic books |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910461730403321 |
Hirsch Morris W. <1933->
|
||
| Waltham, MA, : Academic Press, c2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Differential equations, dynamical systems, and an introduction to chaos / / Morris W. Hirsch, Stephen Smale, Robert L. Devaney [[electronic resource]]
| Differential equations, dynamical systems, and an introduction to chaos / / Morris W. Hirsch, Stephen Smale, Robert L. Devaney [[electronic resource]] |
| Autore | Hirsch Morris W. <1933-> |
| Edizione | [3rd ed.] |
| Pubbl/distr/stampa | Waltham, MA, : Academic Press, c2013 |
| Descrizione fisica | 1 online resource (xiv, 418 p. ) : ill. ; |
| Disciplina | 515/.35 |
| Altri autori (Persone) |
SmaleStephen <1930->
DevaneyRobert L. <1948-> |
| Soggetto topico |
Differential equations
Algebras, Linear Chaotic behavior in systems |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910790003803321 |
|
Hirsch Morris W. <1933->
|
||
| Waltham, MA, : Academic Press, c2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Differential equations, dynamical systems, and an introduction to chaos (Third Edition) / / Morris W. Hirsch, Stephen Smale, Robert L. Devaney
| Differential equations, dynamical systems, and an introduction to chaos (Third Edition) / / Morris W. Hirsch, Stephen Smale, Robert L. Devaney |
| Autore | Hirsch Morris W. <1933-> |
| Edizione | [3rd ed.] |
| Pubbl/distr/stampa | Waltham, MA, : Academic Press, c2013 |
| Descrizione fisica | 1 online resource (xiv, 418 p. ) : ill. ; |
| Disciplina | 515/.35 |
| Altri autori (Persone) |
SmaleStephen <1930->
DevaneyRobert L. <1948-> |
| Soggetto topico |
Differential equations
Algebras, Linear Chaotic behavior in systems |
| Soggetto genere / forma | Electronic books. |
| ISBN | 0-12-382011-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover -- Differential Equations, Dynamical Systems, and an Introduction to Chaos -- Copyright -- Table of Contents -- Preface to Third Edition -- Preface -- 1 First-Order Equations -- 1.1 The Simplest Example -- 1.2 The Logistic Population Model -- 1.3 Constant Harvesting and Bifurcations -- 1.4 Periodic Harvesting and Periodic Solutions -- 1.5 Computing the Poincaré Map -- 1.6 Exploration: A Two-Parameter Family -- Exercises -- 2 Planar Linear Systems -- 2.1 Second-Order Differential Equations -- 2.2 Planar Systems -- 2.3 Preliminaries from Algebra -- 2.4 Planar Linear Systems -- 2.5 Eigenvalues and Eigenvectors -- 2.6 Solving Linear Systems -- 2.7 The Linearity Principle -- Exercises -- 3 Phase Portraits for Planar Systems -- 3.1 Real Distinct Eigenvalues -- 3.2 Complex Eigenvalues -- 3.3 Repeated Eigenvalues -- 3.4 Changing Coordinates -- Exercises -- 4 Classification of Planar Systems -- 4.1 The Trace-Determinant Plane -- 4.2 Dynamical Classification -- Case 1 -- Case 2 -- Case 3 -- 4.3 Exploration: A 3D Parameter Space -- Exercises -- 5 Higher-Dimensional Linear Algebra -- 5.1 Preliminaries from Linear Algebra -- 5.2 Eigenvalues and Eigenvectors -- 5.3 Complex Eigenvalues -- 5.4 Bases and Subspaces -- 5.5 Repeated Eigenvalues -- 5.6 Genericity -- Exercises -- 6 Higher-Dimensional Linear Systems -- 6.1 Distinct Eigenvalues -- 6.2 Harmonic Oscillators -- 6.3 Repeated Eigenvalues -- 6.4 The Exponential of a Matrix -- 6.5 Nonautonomous Linear Systems -- Exercises -- 7 Nonlinear Systems -- 7.1 Dynamical Systems -- 7.2 The Existence and Uniqueness Theorem -- 7.3 Continuous Dependence of Solutions -- 7.4 The Variational Equation -- 7.5 Exploration: Numerical Methods -- 7.6 Exploration: Numerical Methods and Chaos -- Exercises -- 8 Equilibria in Nonlinear Systems -- 8.1 Some Illustrative Examples -- 8.2 Nonlinear Sinks and Sources -- 8.3 Saddles.
8.4 Stability -- 8.5 Bifurcations -- 8.6 Exploration: Complex Vector Fields -- Exercises -- 9 Global Nonlinear Techniques -- 9.1 Nullclines -- 9.2 Stability of Equilibria -- 9.3 Gradient Systems -- 9.4 Hamiltonian Systems -- 9.5 Exploration: The Pendulum with Constant Forcing -- Exercises -- 10 Closed Orbits and Limit Sets -- 10.1 Limit Sets -- 10.2 Local Sections and Flow Boxes -- 10.3 The Poincaré Map -- 10.4 Monotone Sequences in Planar Dynamical Systems -- 10.5 The Poincaré-Bendixson Theorem -- 10.6 Applications of Poincaré-Bendixson -- 10.7 Exploration: Chemical Reactions that Oscillate -- Exercises -- 11 Applications in Biology -- 11.1 Infectious Diseases -- 11.2 Predator-Prey Systems -- 11.3 Competitive Species -- 11.4 Exploration: Competition and Harvesting -- 11.5 Exploration: Adding Zombies to the SIR Model -- Exercises -- 12 Applications in Circuit Theory -- 12.1 An RLC Circuit -- 12.2 The Liénard Equation -- 12.3 The van der Pol Equation -- 12.4 A Hopf Bifurcation -- 12.5 Exploration: Neurodynamics -- Exercises -- 13 Applications in Mechanics -- 13.1 Newton's Second Law -- 13.2 Conservative Systems -- 13.3 Central Force Fields -- 13.4 The Newtonian Central Force System -- 13.5 Kepler's First Law -- 13.6 The Two-Body Problem -- 13.7 Blowing up the Singularity -- 13.8 Exploration: Other Central Force Problems -- 13.9 Exploration: Classical Limits of Quantum Mechanical Systems -- 13.10 Exploration: Motion of a Glider -- Exercises -- 14 The Lorenz System -- 14.1 Introduction -- 14.2 Elementary Properties of the Lorenz System -- 14.3 The Lorenz Attractor -- 14.4 A Model for the Lorenz Attractor -- 14.5 The Chaotic Attractor -- 14.6 Exploration: The Rössler Attractor -- Exercises -- 15 Discrete Dynamical Systems -- 15.1 Introduction -- 15.2 Bifurcations -- 15.3 The Discrete Logistic Model -- 15.4 Chaos -- 15.5 Symbolic Dynamics. 15.6 The Shift Map -- 15.7 The Cantor Middle-Thirds Set -- 15.8 Exploration: Cubic Chaos -- 15.9 Exploration: The Orbit Diagram -- Exercises -- 16 Homoclinic Phenomena -- 16.1 The Shilnikov System -- 16.2 The Horseshoe Map -- 16.3 The Double Scroll Attractor -- 16.4 Homoclinic Bifurcations -- 16.5 Exploration: The Chua Circuit -- Exercises -- 17 Existence and Uniqueness Revisited -- 17.1 The Existence and Uniqueness Theorem -- 17.2 Proof of Existence and Uniqueness -- 17.3 Continuous Dependence on Initial Conditions -- 17.4 Extending Solutions -- 17.5 Nonautonomous Systems -- 17.6 Differentiability of the Flow -- Exercises -- Bibliography -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- K -- L -- M -- N -- O -- P -- R -- S -- T -- U -- V -- W -- Z. |
| Record Nr. | UNINA-9910965872603321 |
|
Hirsch Morris W. <1933->
|
||
| Waltham, MA, : Academic Press, c2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Differential equations, dynamical systems, and linear algebra [[electronic resource] /] / Morris W. Hirsch and Stephen Smale
| Differential equations, dynamical systems, and linear algebra [[electronic resource] /] / Morris W. Hirsch and Stephen Smale |
| Autore | Hirsch Morris W. <1933-> |
| Pubbl/distr/stampa | New York, : Academic Press, 1974 |
| Descrizione fisica | 1 online resource (373 p.) |
| Disciplina |
510.8 s515.35
510/.8 s 515/.35 512.5 515.35 |
| Altri autori (Persone) |
SmaleStephen <1930->
HirschMorris W. <1933-> |
| Collana | Pure and applied mathematics |
| Soggetto topico |
Differential equations
Algebras, Linear |
| ISBN |
1-281-76362-4
9786611763626 0-08-087376-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Front Cover; Differential Equations, Dynamical Systems, and Linear Algebra; Copyright Page; Contents; Preface; CHAPTER 1. FIRST EXAMPLES; 1. The Simplest Examples; 2. Linear Systems with Constant Coefficients; Notes; CHAPTER 2. NEWTON'S EQUATION AND KEPLER'S LAW; 1. Harmonic Oscillators; 2. Some Calculus Background; 3. Conservative Force Fields; 4. Central Force Fields; 5. States; 6. Elliptical Planetary Orbits; Notes; CHAPTER 3. LINEAR SYSTEMS WITH CONSTANT COEFICIENTS AND REAL EIGENVALUES; 1. Basic Linear Algebra; 2. Real Eigenvalues
3. Differential Equations with Real, Distinct Eigenvalues4. Complex Eigenvalues; CHAPTER 4. LINEAR SYSTEMS WITH CONSTANT COEFFICIENTS AND COMPLEX EIGENVALUES; 1. Complex Vector Spaces; 2. Real Operators with Complex Eigenvalues; 3. Application of Complex Linear Algebra to Differential Equations; CHAPTER 5. LINEAR SYSTEMS AND EXPONENTIALS OF OPERATORS; 1. Review of Topology in Rn; 2. New Norms for Old; 3. Exponentials of Operators; 4. Homogeneous Linear Systems; 5. A Nonhomogeneous Equation; 6. Higher Order Systems; Notes; CHAPTER 6. LINEAR SYSTEMS AND CANONICAL FORMS OF OPERATORS 1. The Primary Decomposition2. The S + N Decomposition; 3. Nilpotent Canonical Forms; 4. Jordan and Real Canonical Forms; 5. Canonical Forms and Differential Equations; 6. Higher Order Linear Equations; 7. Operators on Function Spaces; CHAPTER 7. CONTRACTIONS AND GENERIC PROPERTIES OF OPERATORS; 1. Sinks and Sources; 2. Hyperbolic Flows; 3. Generic Properties of Operators; 4. The Significance of Genericity; CHAPTER 8. FUNDAMENTAL THEORY; 1. Dynamical Systems and Vector Fields; 2. The Fundamental Theorem; 3. Existence and Uniqueness; 4. Continuity of Solutions in Initial Conditions 5. On Extending Solutions6. Global Solutions; 7. The Flow of a Differential Equation; Notes; CHAPTER 9. STABILITY OF EQUILIBRIA; 1. Nonlinear Sinks; 2. Stability; 3. Liapunov Functions; 4. Gradient Systems; 5. Gradients and Inner Products; Notes; CHAPTER 10. DIFFERENTIAL EQUATIONS FOR ELECTRICAL CIRCUITS; 1. An RLC Circuit; 2. Analysis of the Circuit Equations; 3. Van der Pol's Equation; 4. Hopf Bifurcation; 5. More General Circuit Equations; Notes; CHAPTER 11. THE POINCARÉ-BENDIXSON THEOREM; 1. Limit Sets; 2. Local Sections and Flow Boxes; 3. Monotone Sequences in Planar Dynamical Systems 4. The Poincaré-Bendixson Theorem5. Applications of the Poincaré-Bendixson Theorem; Notes; CHAPTER 12. ECOLOGY; 1. One Species; 2. Predator and Prey; 3. Competing Species; Notes; CHAPTER 13. PERIODIC ATTRACTORS; 1. Asymptotic Stability of Closed Orbits; 2. Discrete Dynamical Systems; 3. Stability and Closed Orbits; CHAPTER 14. CLASSICAL MECHANICS; 1. The n-Body Problem; 2. Hamiltonian Mechanics; Notes; CHAPTER 15. NONAUTONOMOUS EQUATIONS AND DIFFERENTIABILITY OF FLOWS; 1. Existence, Uniqueness, and Continuity for Nonautonomous Differential Equations 2. Differentiability of the Flow of Autonomous Equations |
| Record Nr. | UNINA-9910782594503321 |
|
Hirsch Morris W. <1933->
|
||
| New York, : Academic Press, 1974 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Invariant manifolds / / M. W. Hirsch, C. C. Pugh, M. Shub
| Invariant manifolds / / M. W. Hirsch, C. C. Pugh, M. Shub |
| Autore | Hirsch Morris W. <1933-> |
| Edizione | [1st ed. 1977.] |
| Pubbl/distr/stampa | Berlin ; ; Heidelberg : , : Springer-Verlag, , [1977] |
| Descrizione fisica | 1 online resource (VI, 150 p.) |
| Disciplina | 514.72 |
| Collana | Lecture Notes in Mathematics |
| Soggetto topico |
Foliations (Mathematics)
Invariant manifolds |
| ISBN | 3-540-37382-9 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | The linear theory of normal hyperbolicity -- The Cr section theorem and lipschitz jets -- The local theory of normally hyperbolic, invariant, compact manifolds -- Pseudo hyperbolicity and plaque families -- Center manifolds -- Noncompactness and uniformity -- Forced smoothness of i: V ? M -- Branched laminations -- Normally hyperbolic foliations and laminations -- Local product structure and local stability -- Equivariant fibrations and nonwandering sets. |
| Record Nr. | UNISA-996466655003316 |
|
Hirsch Morris W. <1933->
|
||
| Berlin ; ; Heidelberg : , : Springer-Verlag, , [1977] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||