Introduction To Arnold S Proof Of The Kolmogorov Arnold Moser Theorem
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Introduction To Arnold S Proof Of The Kolmogorov Arnold Moser Theorem
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Author : Achim Feldmeier
language : en
Publisher:
Release Date : 2022
Introduction To Arnold S Proof Of The Kolmogorov Arnold Moser Theorem written by Achim Feldmeier and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with Kolmogorov-Arnold-Moser theory categories.
"This book provides an accessible step-by-step account of Arnold's classical proof of the Kolmogorov-Arnold-Moser (KAM) Theorem. It begins with a general background of the theorem and proves the famous Liouville-Arnold theorem for integrable systems and introduces Kneser's tori in four-dimensional phase space. It then introduces and discusses the ideas and techniques used in Arnold's proof, before the second half of the book walks the reader through a detailed account of Arnold's proof with all the required steps. It will be a useful guide for advanced students of mathematical physics, in addition to researchers and professionals. Key features: Applies concepts and theorems from real and complex analysis (e.g. Fourier series; implicit function theorem) and topology in the framework of this key theorem from mathematical physics. Covers all aspects of Arnold's proof, including those often left out in more general or simplified presentations. Discusses, in detail, the ideas used in the proof of the KAM theorem and puts them in historical context (e.g. mapping degree from algebraic topology)"--
Introduction To Arnold S Proof Of The Kolmogorov Arnold Moser Theorem
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Author : Achim Feldmeier
language : en
Publisher: CRC Press
Release Date : 2022-07-08
Introduction To Arnold S Proof Of The Kolmogorov Arnold Moser Theorem written by Achim Feldmeier and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-07-08 with Science categories.
INTRODUCTION TO ARNOLD’S PROOF OF THE KOLMOGOROV–ARNOLD–MOSER THEOREM This book provides an accessible step-by-step account of Arnold’s classical proof of the Kolmogorov–Arnold–Moser (KAM) Theorem. It begins with a general background of the theorem, proves the famous Liouville–Arnold theorem for integrable systems and introduces Kneser’s tori in four-dimensional phase space. It then introduces and discusses the ideas and techniques used in Arnold’s proof, before the second half of the book walks the reader through a detailed account of Arnold’s proof with all the required steps. It will be a useful guide for advanced students of mathematical physics, in addition to researchers and professionals. Features • Applies concepts and theorems from real and complex analysis (e.g., Fourier series and implicit function theorem) and topology in the framework of this key theorem from mathematical physics. • Covers all aspects of Arnold’s proof, including those often left out in more general or simplifi ed presentations. • Discusses in detail the ideas used in the proof of the KAM theorem and puts them in historical context (e.g., mapping degree from algebraic topology).
The Kam Story
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Author : H Scott Dumas
language : en
Publisher: World Scientific Publishing Company
Release Date : 2014-02-28
The Kam Story written by H Scott Dumas and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-02-28 with Mathematics categories.
This is a semi-popular mathematics book aimed at a broad readership of mathematically literate scientists, especially mathematicians and physicists who are not experts in classical mechanics or KAM theory, and scientific-minded readers. Parts of the book should also appeal to less mathematically trained readers with an interest in the history or philosophy of science. The scope of the book is broad: it not only describes KAM theory in some detail, but also presents its historical context (thus showing why it was a “breakthrough”). Also discussed are applications of KAM theory (especially to celestial mechanics and statistical mechanics) and the parts of mathematics and physics in which KAM theory resides (dynamical systems, classical mechanics, and Hamiltonian perturbation theory). Although a number of sources on KAM theory are now available for experts, this book attempts to fill a long-standing gap at a more descriptive level. It stands out very clearly from existing publications on KAM theory because it leads the reader through an accessible account of the theory and places it in its proper context in mathematics, physics, and the history of science.
Mathematics Of Complexity And Dynamical Systems
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Author : Robert A. Meyers
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-10-05
Mathematics Of Complexity And Dynamical Systems written by Robert A. Meyers and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-05 with Mathematics categories.
Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.
Action Minimizing Methods In Hamiltonian Dynamics Mn 50
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Author : Alfonso Sorrentino
language : en
Publisher: Princeton University Press
Release Date : 2015-05-26
Action Minimizing Methods In Hamiltonian Dynamics Mn 50 written by Alfonso Sorrentino and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-26 with Mathematics categories.
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.
Measure And Capacity Of Wandering Domains In Gevrey Near Integrable Exact Symplectic Systems
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Author : Laurent Lazzarini
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-02-21
Measure And Capacity Of Wandering Domains In Gevrey Near Integrable Exact Symplectic Systems written by Laurent Lazzarini and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-21 with Domains of holomorphy categories.
A wandering domain for a diffeomorphism of is an open connected set such that for all . The authors endow with its usual exact symplectic structure. An integrable diffeomorphism, i.e., the time-one map of a Hamiltonian which depends only on the action variables, has no nonempty wandering domains. The aim of this paper is to estimate the size (measure and Gromov capacity) of wandering domains in the case of an exact symplectic perturbation of , in the analytic or Gevrey category. Upper estimates are related to Nekhoroshev theory; lower estimates are related to examples of Arnold diffusion. This is a contribution to the “quantitative Hamiltonian perturbation theory” initiated in previous works on the optimality of long term stability estimates and diffusion times; the emphasis here is on discrete systems because this is the natural setting to study wandering domains.
Introduction To Mechanics And Symmetry
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Author : Jerrold E. Marsden
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-19
Introduction To Mechanics And Symmetry written by Jerrold E. Marsden and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-19 with Science categories.
A development of the basic theory and applications of mechanics with an emphasis on the role of symmetry. The book includes numerous specific applications, making it beneficial to physicists and engineers. Specific examples and applications show how the theory works, backed by up-to-date techniques, all of which make the text accessible to a wide variety of readers, especially senior undergraduates and graduates in mathematics, physics and engineering. This second edition has been rewritten and updated for clarity throughout, with a major revamping and expansion of the exercises. Internet supplements containing additional material are also available.
Reports On Astronomy
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Author : Immo Appenzeller
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Reports On Astronomy written by Immo Appenzeller and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
IAU Transactions are published as a volume corresponding to each General Assembly. Volume A is produced prior to the Assembly and contains Reports on Astronomy, prepared by each Commission President. The intention is to summarize the astronomical results that have affected the work of the Commission since the production of the previous Reports up to a time which is about one year prior to the General Assembly. Volume B is produced after the Assembly and contains accounts of Commission Meetings which were held, together with other material. The reports included in the present volume range from outline summaries to lengthy compilations and references. Most reports are in English.
The Kolmogorov Legacy In Physics
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Author : Angelo Vulpiani
language : en
Publisher: Springer
Release Date : 2003-12-12
The Kolmogorov Legacy In Physics written by Angelo Vulpiani and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-12-12 with Science categories.
The present volume, published at the occasion of his 100th birthday anniversary, is a collection of articles that reviews the impact of Kolomogorov's work in the physical sciences and provides an introduction to the modern developments that have been triggered in this way to encompass recent applications in biology, chemistry, information sciences and finance.
Celestial Dynamics
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Author : Rudolf Dvorak
language : en
Publisher: John Wiley & Sons
Release Date : 2013-08-30
Celestial Dynamics written by Rudolf Dvorak and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-30 with Science categories.
Written by an internationally renowned expert author and researcher, this monograph fills the need for a book conveying the sophisticated tools needed to calculate exo-planet motion and interplanetary space flight. It is unique in considering the critical problems of dynamics and stability, making use of the software Mathematica, including supplements for practical use of the formulae. A must-have for astronomers and applied mathematicians alike.