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Action-minimizing methods in Hamiltonian dynamics : an introduction to Aubry-Mather theory / / Alfonso Sorrentino
| Action-minimizing methods in Hamiltonian dynamics : an introduction to Aubry-Mather theory / / Alfonso Sorrentino |
| Autore | Sorrentino Alfonso |
| Edizione | [Pilot project,eBook available to selected US libraries only] |
| Pubbl/distr/stampa | Princeton, [New Jersey] ; ; Oxford, [England] : , : Princeton University Press, , 2015 |
| Descrizione fisica | 1 online resource (129 p.) |
| Disciplina | 514.74 |
| Collana | Mathematical Notes |
| Soggetto topico |
Hamiltonian systems
Hamilton-Jacobi equations |
| Soggetto genere / forma | Electronic books. |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Front matter -- Contents -- Preface -- Chapter One. Tonelli Lagrangians and Hamiltonians on Compact Manifolds -- Chapter Two. From KAM Theory to Aubry-Mather Theory -- Chapter Three. Action-Minimizing Invariant Measures for Tonelli Lagrangians -- Chapter Four. Action-Minimizing Curves for Tonelli Lagrangians -- Chapter Five. The Hamilton-Jacobi Equation and Weak KAM Theory -- Appendices -- Appendix A. On the Existence of Invariant Lagrangian Graphs -- Appendix B. Schwartzman Asymptotic Cycle and Dynamics -- Bibliography -- Index |
| Record Nr. | UNINA-9910463953703321 |
Sorrentino Alfonso
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| Princeton, [New Jersey] ; ; Oxford, [England] : , : Princeton University Press, , 2015 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Action-minimizing methods in Hamiltonian dynamics : an introduction to Aubry-Mather theory / / Alfonso Sorrentino
| Action-minimizing methods in Hamiltonian dynamics : an introduction to Aubry-Mather theory / / Alfonso Sorrentino |
| Autore | Sorrentino Alfonso |
| Edizione | [Pilot project,eBook available to selected US libraries only] |
| Pubbl/distr/stampa | Princeton, [New Jersey] ; ; Oxford, [England] : , : Princeton University Press, , 2015 |
| Descrizione fisica | 1 online resource (129 p.) |
| Disciplina | 514.74 |
| Collana | Mathematical Notes |
| Soggetto topico |
Hamiltonian systems
Hamilton-Jacobi equations |
| Soggetto non controllato |
Albert Fathi
Aubry set AubryЍather theory Hamiltonian dynamics Hamiltonians HamiltonЊacobi equation John Mather KAM theory KAM tori Lagrangian dynamics MAK tori Ma set Ma's critical value Ma's potential Maher sets Peierls' barrier Tonelli Lagrangians action-minimizing measure action-minimizing orbits chaos classical mechanics compact manifold differentiability invariant Lagrangian graphs invariant probability measures invariant sets orbits pendulum stable motion strict convexity unstable motion |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Front matter -- Contents -- Preface -- Chapter One. Tonelli Lagrangians and Hamiltonians on Compact Manifolds -- Chapter Two. From KAM Theory to Aubry-Mather Theory -- Chapter Three. Action-Minimizing Invariant Measures for Tonelli Lagrangians -- Chapter Four. Action-Minimizing Curves for Tonelli Lagrangians -- Chapter Five. The Hamilton-Jacobi Equation and Weak KAM Theory -- Appendices -- Appendix A. On the Existence of Invariant Lagrangian Graphs -- Appendix B. Schwartzman Asymptotic Cycle and Dynamics -- Bibliography -- Index |
| Record Nr. | UNINA-9910788016003321 |
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Sorrentino Alfonso
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||
| Princeton, [New Jersey] ; ; Oxford, [England] : , : Princeton University Press, , 2015 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Action-minimizing methods in Hamiltonian dynamics : an introduction to Aubry-Mather theory / / Alfonso Sorrentino
| Action-minimizing methods in Hamiltonian dynamics : an introduction to Aubry-Mather theory / / Alfonso Sorrentino |
| Autore | Sorrentino Alfonso |
| Edizione | [Pilot project,eBook available to selected US libraries only] |
| Pubbl/distr/stampa | Princeton, [New Jersey] ; ; Oxford, [England] : , : Princeton University Press, , 2015 |
| Descrizione fisica | 1 online resource (129 p.) |
| Disciplina | 514.74 |
| Collana | Mathematical Notes |
| Soggetto topico |
Hamiltonian systems
Hamilton-Jacobi equations |
| Soggetto non controllato |
Albert Fathi
Aubry set AubryЍather theory Hamiltonian dynamics Hamiltonians HamiltonЊacobi equation John Mather KAM theory KAM tori Lagrangian dynamics MAK tori Ma set Ma's critical value Ma's potential Maher sets Peierls' barrier Tonelli Lagrangians action-minimizing measure action-minimizing orbits chaos classical mechanics compact manifold differentiability invariant Lagrangian graphs invariant probability measures invariant sets orbits pendulum stable motion strict convexity unstable motion |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Front matter -- Contents -- Preface -- Chapter One. Tonelli Lagrangians and Hamiltonians on Compact Manifolds -- Chapter Two. From KAM Theory to Aubry-Mather Theory -- Chapter Three. Action-Minimizing Invariant Measures for Tonelli Lagrangians -- Chapter Four. Action-Minimizing Curves for Tonelli Lagrangians -- Chapter Five. The Hamilton-Jacobi Equation and Weak KAM Theory -- Appendices -- Appendix A. On the Existence of Invariant Lagrangian Graphs -- Appendix B. Schwartzman Asymptotic Cycle and Dynamics -- Bibliography -- Index |
| Record Nr. | UNINA-9910812171703321 |
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Sorrentino Alfonso
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||
| Princeton, [New Jersey] ; ; Oxford, [England] : , : Princeton University Press, , 2015 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Generalized solutions of Hamilton-Jacobi equations / P.L. Lions
| Generalized solutions of Hamilton-Jacobi equations / P.L. Lions |
| Autore | Lions, Pierre-Louis |
| Pubbl/distr/stampa | Boston : Pitman Publishing, 1982 |
| Descrizione fisica | 317 p. ; 25 cm. |
| Disciplina | 515.353 |
| Collana | Pitman research notes in mathematics series, ISSN 02693674 ; 69 |
| Soggetto topico |
Cauchy problem
Dirichlet problem Hamilton-Jacobi equations |
| ISBN | 0273085565 |
| Classificazione |
AMS 30-XX
AMS 35F25 AMS 35L60 AMS 49L05 AMS 49L20 AMS 70H20 AMS 93C15 QA374.L484 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISALENTO-991000932709707536 |
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Lions, Pierre-Louis
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| Boston : Pitman Publishing, 1982 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
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The Hamilton-Jacobi equation : a global approach / Stanley H. Benton
| The Hamilton-Jacobi equation : a global approach / Stanley H. Benton |
| Autore | Benton, Stanley H. |
| Pubbl/distr/stampa | New York : Academic Press, 1977 |
| Descrizione fisica | xi, 147 p. ; 24 cm |
| Disciplina | 515.35 |
| Collana | Mathematics in science and engineering. A series of monographs and textbooks, 0076-5392 ; 131 |
| Soggetto topico |
Hamilton-Jacobi equations
Mechanics of particles and systems |
| ISBN | 0120893509 |
| Classificazione |
AMS 70-02
AMS 70-XX AMS 70H20 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISALENTO-991000970999707536 |
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Benton, Stanley H.
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| New York : Academic Press, 1977 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
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Hamilton-Jacobi equations in Hilbert spaces / V. Barbu, G. Da Prato
| Hamilton-Jacobi equations in Hilbert spaces / V. Barbu, G. Da Prato |
| Autore | Barbu, Viorel |
| Pubbl/distr/stampa | Boston : Pitman Advanced Publ. Program, 1983 |
| Descrizione fisica | 172 p. ; 24 cm |
| Disciplina | 515.35 |
| Altri autori (Persone) | Da Prato, Giuseppe |
| Collana | Pitman research notes in mathematics series, ISSN 02693674 ; 86 |
| Soggetto topico |
Hamilton-Jacobi equations
Hilbert spaces Initial value problems |
| ISBN | 0273085972 |
| Classificazione |
AMS 34G
LC QA378.B37 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISALENTO-991000971049707536 |
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Barbu, Viorel
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| Boston : Pitman Advanced Publ. Program, 1983 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
| ||
Linear and regular celestial mechanics : perturbed two-body motion, numerical methods, canonical theory / E. L. Stiefel, G. Scheifele
| Linear and regular celestial mechanics : perturbed two-body motion, numerical methods, canonical theory / E. L. Stiefel, G. Scheifele |
| Autore | Stiefel, Eduard L. |
| Pubbl/distr/stampa | Berlin : Springer-Verlag, 1971 |
| Descrizione fisica | ix, 301 p. : ill. ; 24 cm. |
| Disciplina | 521 |
| Altri autori (Persone) | Scheifele, G. |
| Collana | Grundlehren der mathematischen Wissenschaften = A series of comprehensive studies in mathematics, 0072-7830 ; 174 |
| Soggetto topico |
Celestial mechanics
Hamilton-Jacobi equations Orbital mechanics Two-body problem |
| ISBN | 3540051198 |
| Classificazione |
AMS 70F05
AMS 70F15 AMS 70H15 AMS 70H20 AMS 70M20 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISALENTO-991001085829707536 |
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Stiefel, Eduard L.
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| Berlin : Springer-Verlag, 1971 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
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On Modern Approaches of Hamilton-Jacobi Equations and Control Problems with Discontinuities : A Guide to Theory, Applications, and Some Open Problems / / Guy Barles and Emmanuel Chasseigne
| On Modern Approaches of Hamilton-Jacobi Equations and Control Problems with Discontinuities : A Guide to Theory, Applications, and Some Open Problems / / Guy Barles and Emmanuel Chasseigne |
| Autore | Barles Guy |
| Edizione | [First edition.] |
| Pubbl/distr/stampa | Cham, Switzerland : , : the under published is book, , [2024] |
| Descrizione fisica | 1 online resource (569 pages) |
| Disciplina | 515.353 |
| Collana | Progress in Nonlinear Differential Equations and Their Applications Series |
| Soggetto topico |
Differential equations, Partial
Hamilton-Jacobi equations |
| ISBN | 3-031-49371-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Acknowledgements: -- Survival kit for the potential reader: how can this book be useful to you? -- Additional information: -- Notations and Terminology -- Contents -- Introduction -- Viscosity solutions and discontinuities -- A simple, universal, and efficient notion of solution -- Discontinuities, a potential weakness of viscosity solutions -- The end of universality? -- Toward more general discontinuities -- Networks -- Key considerations related to discontinuities -- Overview of the content -- Part I A Toolbox for Discontinuous Hamilton-Jacobi Equations and Control Problems -- Chapter 1 The Basic Continuous Framework Revisited -- 1.1 The value function and the associated PDE -- 1.2 Important remarks on the comparison proof -- 1.3 Basic assumptions -- Chapter 2 PDE Tools -- 2.1 Discontinuous viscosity solutions for equations with discontinuities -- 2.1.1 Discontinuous viscosity solutions -- 2.1.2 The half-relaxed limits method -- 2.2 Strong comparison results: how to cook them? -- 2.2.1 Stationary equations -- 2.2.2 The evolution case -- 2.2.3 Viscosity inequalities at = in the evolution case -- 2.2.4 The simplest examples of comparison results: the continuous case -- 2.3 Whitney stratifications -- 2.3.1 General and admissible flat stratifications -- 2.3.2 Locally flattenable stratifications -- 2.3.3 Limits of the (LFS) approach -- 2.3.4 Tangentially flattenable stratifications -- 2.4 Partial regularity, partial regularization -- 2.4.1 Regular discontinuous functions -- 2.4.2 Regularity of subsolutions -- 2.4.3 Regularization of subsolutions -- 2.4.4 What about regularization for supersolutions? -- 2.5 Sub- and superdifferentials, inequalities at the boundary -- Chapter 3 Control Tools -- 3.1 Introduction: how to define deterministic control problems with discontinuities? The two half-spaces problem.
3.2 A general framework for deterministic control problems -- 3.2.1 Dynamics, discounts, and costs -- 3.2.2 The control problem -- 3.2.3 The value function -- 3.3 Ishii solutions for the Bellman Equation -- 3.3.1 Discontinuous viscosity solutions -- 3.3.2 The dynamic programming principle -- 3.3.3 The value function is an Ishii solution -- 3.4 Supersolutions of the Bellman Equation -- 3.4.1 The super-dynamic programming principle -- 3.4.2 The value function is the minimal supersolution -- Chapter 4 Mixed Tools -- 4.1 Initial conditions for suband supersolutions of the Bellman Equation -- 4.1.1 The general result -- 4.1.2 A relevant example involving unbounded control -- 4.2 The sub-dynamic programming principle for subsolutions -- 4.3 Local comparison for discontinuous HJB Equations -- 4.4 The "good framework for HJ Equations with discontinuities" -- 4.4.1 General definition at the PDE level -- 4.4.2 The stratified case, "good assumptions" on the control problem -- 4.4.3 Ishii solutions for a codimension-1 discontinuous Hamilton-Jacobi Equation -- Chapter 5 Other Tools -- 5.1 Semiconvex and semiconcave functions: the main properties -- 5.2 Quasiconvexity: definition and main properties -- 5.2.1 Quasiconvex functions on the real line -- 5.2.2 On the maximum of two quasiconvex functions -- 5.2.3 Application to quasiconvex Hamiltonians -- 5.3 A strange, Kirchhoff-related lemma -- 5.4 A few results for penalized problems -- 5.4.1 The compact case -- 5.4.2 Penalization at infinity -- Part II Deterministic Control Problems and Hamilton-Jacobi Equations for Codimension-1 Discontinuities -- Chapter 6 Introduction: Ishii Solutions for the Hyperplane Case -- 6.1 The PDE viewpoint -- 6.2 The control viewpoint -- 6.3 The uniqueness question -- Chapter 7 The Control Problem and the "Natural" Value Function -- 7.1 Finding trajectories by differential inclusions. 7.2 The Uvalue function -- 7.3 The complementary equation -- 7.4 A characterization of U- -- Chapter 8 A Less Natural Value Function, Regular Dynamics -- 8.1 Introducing U+ -- 8.2 More on regular trajectories -- 8.3 A Magical Lemma for U+ -- 8.4 Maximality of U+ -- 8.5 Appendix: stability of regular trajectories -- Chapter 9 Uniqueness and Non-Uniqueness Features -- 9.1 A typical example where U+ U− -- 9.2 Equivalent definitions for and reg -- 9.3 A sufficient condition to get uniqueness -- 9.4 More examples of uniqueness and non-uniqueness -- Chapter 10 Adding a Specific Problem to the Interface -- 10.1 The control problem -- 10.2 The minimal solution -- 10.3 The maximal solution -- Chapter 11 Remarks on the Uniqueness Proofs, Problems Without Controllability -- 11.1 The main steps of the uniqueness proofs and the role of the normal controllability -- 11.2 Some problems without controllability -- Chapter 12 Further Discussions and Open Problems -- 12.1 The Ishii subsolution inequality: natural or unnatural from the control point-of-view? -- 12.2 Infinite horizon control problems and stationary equations -- 12.3 Towards more general discontinuities: a bunch of open problems. -- 12.3.1 Non-uniqueness in the case of codimension discontinuities -- 12.3.2 Puzzling examples -- Part III Hamilton-Jacobi Equations with Codimension-1 Discontinuities: the "Network Point-of-View" -- Chapter 13 Introduction -- 13.1 The "network approach": a different point-of-view -- 13.1.1 A larger space of test-functions -- 13.1.2 Different types of junction conditions -- 13.2 The "good assumptions" used in Part III -- 13.2.1 Good assumptions on 1, 2 -- 13.2.2 Good assumptions on the junction condition -- 13.3 What do we do in this part? -- Chapter 14 Flux-Limited Solutions for Control Problems and Quasiconvex Hamiltonians -- 14.1 Definition and first properties. 14.2 Stability of flux-limited solutions -- 14.3 Comparison results for flux-limited solutions and applications -- 14.3.1 The convex case -- 14.3.2 The quasiconvex case -- 14.4 Flux-limited solutions and control problems -- 14.5 Vanishing viscosity approximation (I): convergence via flux-limited solutions -- 14.6 Classical viscosity solutions as flux-limited solutions -- 14.7 Extension to second-order equations (I) -- Chapter 15 Junction Viscosity Solutions -- 15.1 Definition and first properties -- 15.1.1 Lack of regularity of subsolutions -- 15.1.2 The case of Kirchhoff-type conditions -- 15.2 Stability of junction viscosity solutions -- 15.3 Comparison results for junction viscosity solutions: the Lions-Souganidis approach -- 15.3.1 Preliminary lemmas -- 15.3.2 A comparison result for the Kirchhoff condition -- 15.3.3 Remarks on the comparison proof and some possible variations -- 15.3.4 Comparison results for more general junction conditions -- 15.3.5 Extension to second-order problems (II) -- 15.4 Vanishing viscosity approximation (II): convergence via junction viscosity solutions -- Chapter 16 From One Notion of Solution to the Others -- 16.1 Ishii and flux-limited solutions -- 16.2 Flux-limited and junction viscosity solutions for flux-limited conditions -- 16.3 The Kirchhoff condition and flux limiters -- 16.4 General Kirchhoff conditions and flux limiters -- 16.5 Vanishing viscosity approximation (III) -- 16.6 A few words about existence -- 16.7 Where the equivalence helps to pass to the limit -- Chapter 17 Emblematic Examples -- 17.1 HJ analog of a discontinuous one-dimensional scalar conservation law -- 17.1.1 On the condition at the interface -- 17.1.2 Network viscosity solutions -- 17.1.3 Main results -- 17.2 Traffic flow models with a fixed or moving flow constraint -- 17.2.1 The LWR model -- 17.2.2 Constraints on the flux. Chapter 18 Further Discussions and Open Problems -- Part IV General Discontinuities: Stratified Problems -- Chapter 19 Stratified Solutions -- 19.1 Introduction -- 19.2 Definition of weak and strong stratified solutions -- 19.3 The regularity of strong stratified subsolutions -- 19.4 The comparison result -- 19.5 Regular weak stratified subsolutions are strong stratified subsolutions -- Chapter 20 Connections with Control Problems and Ishii Solutions -- 20.1 Value functions as stratified solutions -- 20.2 Stratified solutions and classical Ishii viscosity solutions -- 20.2.1 The stratified solution as the minimal Ishii solution -- 20.2.2 Ishii subsolutions as stratified subsolutions -- 20.3 Concrete situations that fit into the stratified framework -- 20.3.1 A general control-oriented framework -- 20.3.2 A general PDE-oriented framework -- Chapter 21 Stability Results -- 21.1 Strong convergence of stratifications when the local structure is unchanged -- 21.2 Weak convergence of stratifications and the associated stability result -- 21.2.1 A half-relaxed limits type result for weakly converging stratifications -- 21.2.2 Some problematic examples -- 21.2.3 Sufficient conditions for stability -- 21.3 Stability under structural modifications of the stratification -- 21.3.1 Introducing new parts of the stratification -- 21.3.2 Eliminable parts of the stratification -- 21.3.3 Sub- and super-stratified problems: a general stability result -- Chapter 22 Applications and Extensions -- 22.1 A crystal growth model-where the stratified formulation is needed -- 22.1.1 Ishii solutions -- 22.1.2 The stratified formulation -- 22.1.3 Generalization -- 22.2 Combustion-where the stratified formulation may unexpectedly help -- 22.2.1 The level set approach -- 22.2.2 The stratified formulation -- 22.2.3 Asymptotic analysis -- 22.3 Large time behavior. 22.3.1 A short overview of the periodic case. |
| Record Nr. | UNINA-9910799203803321 |
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Barles Guy
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| Cham, Switzerland : , : the under published is book, , [2024] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Relazioni simplettiche : la trasformazione di Legendre e la teoria di Hamilton-Jacobi / S. Benenti
| Relazioni simplettiche : la trasformazione di Legendre e la teoria di Hamilton-Jacobi / S. Benenti |
| Autore | Benenti, S. |
| Pubbl/distr/stampa | Bologna : Pitagora, 1988 |
| Descrizione fisica | xi, 335 p. ; 24 cm |
| Disciplina | 530.15 |
| Collana | Quaderni dell'Unione Matematica Italiana ; 33 |
| Soggetto topico | Hamilton-Jacobi equations |
| ISBN | 8837104405 |
| Classificazione | AMS 70H20 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | ita |
| Record Nr. | UNISALENTO-991001295879707536 |
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Benenti, S.
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| Bologna : Pitagora, 1988 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
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Semiconcave functions, Hamilton-Jacobi equations, and optimal control / Piermarco Cannarsa, Carlo Sinestrari
| Semiconcave functions, Hamilton-Jacobi equations, and optimal control / Piermarco Cannarsa, Carlo Sinestrari |
| Autore | Cannarsa, Piermarco |
| Pubbl/distr/stampa | Boston ; Basel ; Berlin : Birkhäuser, c2004 |
| Descrizione fisica | ix, 304 p. ; 24 cm |
| Disciplina | 515.355 |
| Altri autori (Persone) | Sinestrari, Carloauthor |
| Collana | Progress in nonlinear differential equations and their applications ; 58 |
| Soggetto topico |
Concave functions
Hamilton-Jacobi equations Control theory Mathematical optimization |
| ISBN | 0817640843 |
| Classificazione |
AMS 49-02
LC QA353.C64C36 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISALENTO-991002616349707536 |
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Cannarsa, Piermarco
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| Boston ; Basel ; Berlin : Birkhäuser, c2004 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
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