Action-minimizing Methods in Hamiltonian Dynamics (MN-50) : : An Introduction to Aubry-Mather Theory / / Alfonso Sorrentino.
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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Sorrentino, Alfonso, author. aut http://id.loc.gov/vocabulary/relators/aut Action-minimizing Methods in Hamiltonian Dynamics (MN-50) : An Introduction to Aubry-Mather Theory / Alfonso Sorrentino. Pilot project,eBook available to selected US libraries only Princeton, NJ : Princeton University Press, [2015] ©2015 1 online resource (128 p.) : 4 line illus. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Mathematical Notes ; 50 Frontmatter -- 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 restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star 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. Issued also in print. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022) Hamiltonian systems. Mechanics. MATHEMATICS / Applied. bisacsh 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. Title is part of eBook package: De Gruyter Princeton Mathematical Notes eBook-Package 1970-2016 9783110494921 ZDB-23-PMN Title is part of eBook package: De Gruyter Princeton University Press Complete eBook-Package 2014-2015 9783110665925 print 9780691164502 https://doi.org/10.1515/9781400866618 https://www.degruyter.com/isbn/9781400866618 Cover https://www.degruyter.com/document/cover/isbn/9781400866618/original |
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Sorrentino, Alfonso, Sorrentino, Alfonso, |
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Sorrentino, Alfonso, Sorrentino, Alfonso, Action-minimizing Methods in Hamiltonian Dynamics (MN-50) : An Introduction to Aubry-Mather Theory / Mathematical Notes ; Frontmatter -- 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 |
author_facet |
Sorrentino, Alfonso, Sorrentino, Alfonso, |
author_variant |
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Sorrentino, Alfonso, |
title |
Action-minimizing Methods in Hamiltonian Dynamics (MN-50) : An Introduction to Aubry-Mather Theory / |
title_sub |
An Introduction to Aubry-Mather Theory / |
title_full |
Action-minimizing Methods in Hamiltonian Dynamics (MN-50) : An Introduction to Aubry-Mather Theory / Alfonso Sorrentino. |
title_fullStr |
Action-minimizing Methods in Hamiltonian Dynamics (MN-50) : An Introduction to Aubry-Mather Theory / Alfonso Sorrentino. |
title_full_unstemmed |
Action-minimizing Methods in Hamiltonian Dynamics (MN-50) : An Introduction to Aubry-Mather Theory / Alfonso Sorrentino. |
title_auth |
Action-minimizing Methods in Hamiltonian Dynamics (MN-50) : An Introduction to Aubry-Mather Theory / |
title_alt |
Frontmatter -- 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 |
title_new |
Action-minimizing Methods in Hamiltonian Dynamics (MN-50) : |
title_sort |
action-minimizing methods in hamiltonian dynamics (mn-50) : an introduction to aubry-mather theory / |
series |
Mathematical Notes ; |
series2 |
Mathematical Notes ; |
publisher |
Princeton University Press, |
publishDate |
2015 |
physical |
1 online resource (128 p.) : 4 line illus. Issued also in print. |
edition |
Pilot project,eBook available to selected US libraries only |
contents |
Frontmatter -- 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 |
isbn |
9781400866618 9783110494921 9783110665925 9780691164502 |
callnumber-first |
Q - Science |
callnumber-subject |
QA - Mathematics |
callnumber-label |
QA614 |
callnumber-sort |
QA 3614.83 |
url |
https://doi.org/10.1515/9781400866618 https://www.degruyter.com/isbn/9781400866618 https://www.degruyter.com/document/cover/isbn/9781400866618/original |
illustrated |
Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
530 - Physics |
dewey-ones |
531 - Classical mechanics; solid mechanics |
dewey-full |
531.0151539 |
dewey-sort |
3531.0151539 |
dewey-raw |
531.0151539 |
dewey-search |
531.0151539 |
doi_str_mv |
10.1515/9781400866618 |
oclc_num |
979630235 |
work_keys_str_mv |
AT sorrentinoalfonso actionminimizingmethodsinhamiltoniandynamicsmn50anintroductiontoaubrymathertheory |
status_str |
n |
ids_txt_mv |
(DE-B1597)459971 (OCoLC)979630235 |
carrierType_str_mv |
cr |
hierarchy_parent_title |
Title is part of eBook package: De Gruyter Princeton Mathematical Notes eBook-Package 1970-2016 Title is part of eBook package: De Gruyter Princeton University Press Complete eBook-Package 2014-2015 |
is_hierarchy_title |
Action-minimizing Methods in Hamiltonian Dynamics (MN-50) : An Introduction to Aubry-Mather Theory / |
container_title |
Title is part of eBook package: De Gruyter Princeton Mathematical Notes eBook-Package 1970-2016 |
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1806143605898739712 |
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