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Record Nr. |
UNINA9910812171703321 |
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Autore |
Sorrentino Alfonso |
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Titolo |
Action-minimizing methods in Hamiltonian dynamics : an introduction to Aubry-Mather theory / / Alfonso Sorrentino |
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Pubbl/distr/stampa |
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Princeton, [New Jersey] ; ; Oxford, [England] : , : Princeton University Press, , 2015 |
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©2015 |
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Edizione |
[Pilot project,eBook available to selected US libraries only] |
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Descrizione fisica |
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1 online resource (129 p.) |
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Collana |
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Mathematical Notes ; ; 50 |
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Disciplina |
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Soggetti |
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Hamiltonian systems |
Hamilton-Jacobi equations |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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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 |
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Sommario/riassunto |
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John Mather's seminal works in Hamiltonian dynamics represent some of the most important contributions to our understanding of the complex balance between stable and unstable motions in classical mechanics. His novel approach-known as Aubry-Mather theory-singles out the existence of special orbits and invariant measures of the system, which possess a very rich dynamical and geometric structure. In particular, the associated invariant sets play a leading role in determining the global dynamics of the system. This book provides a comprehensive introduction to Mather's theory, and can serve as an interdisciplinary bridge for researchers and students from different fields seeking to acquaint themselves with the topic.Starting with the mathematical background from which Mather's theory was born, |
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