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  3. Dynamik og statik

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

Af: Vadim Kaloshin, Ke Zhang Engelsk Paperback

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

Af: Vadim Kaloshin, Ke Zhang Engelsk Paperback
Tjek vores konkurrenters priser

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.

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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.

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Produktdetaljer
Sprog: Engelsk
Sider: 218
ISBN-13: 9780691202525
Indbinding: Paperback
Udgave:
ISBN-10: 0691202524
Kategori: Dynamik og statik
Udg. Dato: 3 nov 2020
Længde: 16mm
Bredde: 234mm
Højde: 156mm
Forlag: Princeton University Press
Oplagsdato: 3 nov 2020
Forfatter(e): Vadim Kaloshin, Ke Zhang
Forfatter(e) Vadim Kaloshin, Ke Zhang

Kategori Dynamik og statik

ISBN-13 9780691202525

Sprog Engelsk

Indbinding Paperback

Sider 218

Udgave

Længde 16mm

Bredde 234mm

Højde 156mm

Udg. Dato 3 nov 2020

Oplagsdato 3 nov 2020

Forlag Princeton University Press

Kategori sammenhænge