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Author :
Release : 2015
Genre :
Kind : eBook
Book Rating : /5 ( reviews)
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:
Author : Vadim Kaloshin
Release : 2020-11-03
Genre : Science
Kind : eBook
Book Rating : 934/5 ( reviews)
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.
Author : Albert Fathi
Release : 2024-05-09
Genre : Mathematics
Kind : eBook
Book Rating : 70X/5 ( reviews)
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.
Author : Vadim Kaloshin
Release : 2020-11-03
Genre : Mathematics
Kind : eBook
Book Rating : 524/5 ( reviews)
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.
Author : B. V. Čirikov
Release : 1996
Genre :
Kind : eBook
Book Rating : /5 ( reviews)
Book Synopsis Diffuzija Arnolʹda V Bolʹšich Sistemach by : B. V. Čirikov
Download or read book Diffuzija Arnolʹda V Bolʹšich Sistemach written by B. V. Čirikov. This book was released on 1996. Available in PDF, EPUB and Kindle. Book excerpt:
