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Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom – (AMS-208) - Princeton Scholarship Online
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Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom: (AMS-208)

Vadim Kaloshin and Ke Zhang

Abstract

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. This book provides the first complete proof of Arnold diffusion, demonstrating that that there is topological instability for typical perturbations of five ... More

Keywords: Arnold diffusion, dynamical systems, mathematical physics, classical mechanics, Vladimir Arnold, John Mather, Hamiltonian systems, normal forms theory, hyperbolic theory, Mather theory

Bibliographic Information

Print publication date: 2020 Print ISBN-13: 9780691202525
Published to Princeton Scholarship Online: May 2021 DOI:10.23943/princeton/9780691202525.001.0001

Authors

Affiliations are at time of print publication.

Vadim Kaloshin, author
University of Maryland, College Park

Ke Zhang, author
University of Toronto