Vadim Kaloshin

(Author)

Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom: (Ams-208)Paperback, 3 November 2020

Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom: (Ams-208)
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Part of Series
Annals of Mathematics Studies
Part of Series
Annals of Mathematics Studies, 391
Part of Series
Annals of Mathematics Studies, 384
Print Length
224 pages
Language
English
Publisher
Princeton University Press
Date Published
3 Nov 2020
ISBN-10
0691202524
ISBN-13
9780691202525

Description

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.

Product Details

Authors:
Vadim KaloshinKe Zhang
Book Format:
Paperback
Country of Origin:
US
Date Published:
3 November 2020
Dimensions:
23.11 x 15.49 x 1.52 cm
ISBN-10:
0691202524
ISBN-13:
9780691202525
Language:
English
Location:
Princeton
Pages:
224
Weight:
385.55 gm

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