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Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom

2020-11-03 Science
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Release : 2020-11-03
Genre : Science
Kind : eBook
Book Rating : 934/5 ( reviews)

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Book Synopsis Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom by : Vadim Kaloshin

Download or read book Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom written by Vadim Kaloshin. This book was released on 2020-11-03. Available in PDF, EPUB and Kindle. Book excerpt: The first complete proof of Arnold diffusion—one of the most important problems in dynamical systems and mathematical physics Arnold diffusion, which concerns the appearance of chaos in classical mechanics, is one of the most important problems in the fields of dynamical systems and mathematical physics. Since it was discovered by Vladimir Arnold in 1963, it has attracted the efforts of some of the most prominent researchers in mathematics. The question is whether a typical perturbation of a particular system will result in chaotic or unstable dynamical phenomena. In this groundbreaking book, Vadim Kaloshin and Ke Zhang provide the first complete proof of Arnold diffusion, demonstrating that that there is topological instability for typical perturbations of five-dimensional integrable systems (two and a half degrees of freedom). This proof realizes a plan John Mather announced in 2003 but was unable to complete before his death. Kaloshin and Zhang follow Mather's strategy but emphasize a more Hamiltonian approach, tying together normal forms theory, hyperbolic theory, Mather theory, and weak KAM theory. Offering a complete, clean, and modern explanation of the steps involved in the proof, and a clear account of background material, this book is designed to be accessible to students as well as researchers. The result is a critical contribution to mathematical physics and dynamical systems, especially Hamiltonian systems.

Arnold Diffusion for Smooth Convex Systems of Two and a Half Degrees of Freedom

2015
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Release : 2015
Genre :
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis Arnold Diffusion for Smooth Convex Systems of Two and a Half Degrees of Freedom by :

Download or read book Arnold Diffusion for Smooth Convex Systems of Two and a Half Degrees of Freedom written by . This book was released on 2015. Available in PDF, EPUB and Kindle. Book excerpt:

Hamiltonian Systems

2024-05-09 Mathematics
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Release : 2024-05-09
Genre : Mathematics
Kind : eBook
Book Rating : 70X/5 ( reviews)

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Book Synopsis Hamiltonian Systems by : Albert Fathi

Download or read book Hamiltonian Systems written by Albert Fathi. This book was released on 2024-05-09. Available in PDF, EPUB and Kindle. Book excerpt: Dynamical systems that are amenable to formulation in terms of a Hamiltonian function or operator encompass a vast swath of fundamental cases in applied mathematics and physics. This carefully edited volume represents work carried out during the special program on Hamiltonian Systems at MSRI in the Fall of 2018. Topics covered include KAM theory, polygonal billiards, Arnold diffusion, quantum hydrodynamics, viscosity solutions of the Hamilton–Jacobi equation, surfaces of locally minimal flux, Denjoy subsystems and horseshoes, and relations to symplectic topology.

Topics in Dynamics and Ergodic Theory

2003-12-08 Mathematics
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Release : 2003-12-08
Genre : Mathematics
Kind : eBook
Book Rating : 652/5 ( reviews)

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Book Synopsis Topics in Dynamics and Ergodic Theory by : Sergey Bezuglyi

Download or read book Topics in Dynamics and Ergodic Theory written by Sergey Bezuglyi. This book was released on 2003-12-08. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a collection of survey papers by leading researchers in ergodic theory, low-dimensional and topological dynamics and it comprises nine chapters on a range of important topics. These include: the role and usefulness of ultrafilters in ergodic theory, topological dynamics and Ramsey theory; topological aspects of kneading theory together with an analogous 2-dimensional theory called pruning; the dynamics of Markov odometers, Bratteli-Vershik diagrams and orbit equivalence of non-singular automorphisms; geometric proofs of Mather's connecting and accelerating theorems; recent results in one dimensional smooth dynamics; periodic points of nonexpansive maps; arithmetic dynamics; the defect of factor maps; entropy theory for actions of countable amenable groups.

Kam Story, The: A Friendly Introduction To The Content, History, And Significance Of Classical Kolmogorov-arnold-moser Theory

2014-02-28 Mathematics
Download Kam Story, The: A Friendly Introduction To The Content, History, And Significance Of Classical Kolmogorov-arnold-moser Theory PDF Online Free

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Release : 2014-02-28
Genre : Mathematics
Kind : eBook
Book Rating : 602/5 ( reviews)

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Book Synopsis Kam Story, The: A Friendly Introduction To The Content, History, And Significance Of Classical Kolmogorov-arnold-moser Theory by : H Scott Dumas

Download or read book Kam Story, The: A Friendly Introduction To The Content, History, And Significance Of Classical Kolmogorov-arnold-moser Theory written by H Scott Dumas. This book was released on 2014-02-28. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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