Franklin

Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom : (AMS-208) / Ke Zhang, Vadim Kaloshin.

Author/Creator:
Kaloshin, Vadim, author., Author,
Publication:
Princeton, NJ : Princeton University Press, [2020]
Series:
Annals of Mathematics Studies ; 391
Format/Description:
Book
1 online resource (224 pages) : 21 b/w illustrations.
Subjects:
Diffusion -- Mathematical models.
Hamiltonian systems.
Local subjects:
Arnold's paper.
Hamiltonian system.
KAM theorem.
action variables.
autonomous Hamiltonian system.
celestial mechanics.
conservation of action variables.
instability of dynamical systems.
integrable Hamiltonian systems.
linearly stable.
magnetic fields.
motion of charged particles.
negligible friction.
non integrable.
perturb.
several degrees of freedom.
stable solution.
Language:
In English.
System Details:
Mode of access: Internet via World Wide Web.
text file PDF
Summary:
The first complete proof of Arnold diffusion-one of the most important problems in dynamical systems and mathematical physicsArnold 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.
Contents:
Frontmatter
Contents
Preface
Acknowledgments
I. Introduction and the general scheme
II. Forcing relation and Aubry-Mather type
III. Proving forcing equivalence
IV. Supplementary topics
Appendix: Notations
References
Notes:
Description based on online resource; title from PDF title page (publisher's Web site, viewed 25. Nov 2020)
Contributor:
Zhang, Ke, author., Author,
De Gruyter.
Contained In:
De Gruyter University Press Library.
ISBN:
9780691204932
Publisher Number:
10.1515/9780691204932 doi
Access Restriction:
Restricted for use by site license.
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