Action-minimizing Methods in Hamiltonian Dynamics: An Introduction to Aubry-Mather Theory
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 orb...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Princeton
Princeton University Press
2015
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| Schriftenreihe: | Mathematical Notes
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| Schlagworte: | |
| Zusammenfassung: | 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, Alfonso Sorrentino first focuses on the core questions the theory aims to answer-notably the destiny of broken invariant KAM tori and the onset of chaos-and describes how it can be viewed as a natural counterpart of KAM theory. He achieves this by guiding readers through a detailed illustrative example, which also provides the basis for introducing the main ideas and concepts of the general theory. Sorrentino then describes the whole theory and its subsequent developments and applications in their full generality. Shedding new light on John Mather's revolutionary ideas, this book is certain to become a foundational text in the modern study of Hamiltonian systems |
| Beschreibung: | Description based on publisher supplied metadata and other sources |
| Beschreibung: | 1 online resource (128 pages) |
| ISBN: | 9781400866618 9780691164502 |
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| spelling | Sorrentino, Alfonso Verfasser aut Action-minimizing Methods in Hamiltonian Dynamics An Introduction to Aubry-Mather Theory Princeton Princeton University Press 2015 © 2015 1 online resource (128 pages) txt rdacontent c rdamedia cr rdacarrier Mathematical Notes Description based on publisher supplied metadata and other sources 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, Alfonso Sorrentino first focuses on the core questions the theory aims to answer-notably the destiny of broken invariant KAM tori and the onset of chaos-and describes how it can be viewed as a natural counterpart of KAM theory. He achieves this by guiding readers through a detailed illustrative example, which also provides the basis for introducing the main ideas and concepts of the general theory. Sorrentino then describes the whole theory and its subsequent developments and applications in their full generality. Shedding new light on John Mather's revolutionary ideas, this book is certain to become a foundational text in the modern study of Hamiltonian systems Hamiltonian systems Hamilton-Jacobi equations Erscheint auch als Druck-Ausgabe Sorrentino, Alfonso Action-minimizing Methods in Hamiltonian Dynamics : An Introduction to Aubry-Mather Theory |
| spellingShingle | Sorrentino, Alfonso Action-minimizing Methods in Hamiltonian Dynamics An Introduction to Aubry-Mather Theory Hamiltonian systems Hamilton-Jacobi equations |
| title | Action-minimizing Methods in Hamiltonian Dynamics An Introduction to Aubry-Mather Theory |
| title_auth | Action-minimizing Methods in Hamiltonian Dynamics An Introduction to Aubry-Mather Theory |
| title_exact_search | Action-minimizing Methods in Hamiltonian Dynamics An Introduction to Aubry-Mather Theory |
| title_full | Action-minimizing Methods in Hamiltonian Dynamics An Introduction to Aubry-Mather Theory |
| title_fullStr | Action-minimizing Methods in Hamiltonian Dynamics An Introduction to Aubry-Mather Theory |
| title_full_unstemmed | Action-minimizing Methods in Hamiltonian Dynamics An Introduction to Aubry-Mather Theory |
| title_short | Action-minimizing Methods in Hamiltonian Dynamics |
| title_sort | action minimizing methods in hamiltonian dynamics an introduction to aubry mather theory |
| title_sub | An Introduction to Aubry-Mather Theory |
| topic | Hamiltonian systems Hamilton-Jacobi equations |
| topic_facet | Hamiltonian systems Hamilton-Jacobi equations |
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