Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom : : (AMS-208) / / Ke Zhang, Vadim Kaloshin.
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 phys...
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Superior document: | Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2020 English |
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Place / Publishing House: | Princeton, NJ : : Princeton University Press, , [2020] ©2020 |
Year of Publication: | 2020 |
Language: | English |
Series: | Annals of Mathematics Studies ;
384 |
Online Access: | |
Physical Description: | 1 online resource (224 p.) :; 21 b/w illus. |
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100 | 1 | |a Kaloshin, Vadim, |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
245 | 1 | 0 | |a Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom : |b (AMS-208) / |c Ke Zhang, Vadim Kaloshin. |
264 | 1 | |a Princeton, NJ : |b Princeton University Press, |c [2020] | |
264 | 4 | |c ©2020 | |
300 | |a 1 online resource (224 p.) : |b 21 b/w illus. | ||
336 | |a text |b txt |2 rdacontent | ||
337 | |a computer |b c |2 rdamedia | ||
338 | |a online resource |b cr |2 rdacarrier | ||
347 | |a text file |b PDF |2 rda | ||
490 | 0 | |a Annals of Mathematics Studies ; |v 384 | |
505 | 0 | 0 | |t Frontmatter -- |t Contents -- |t Preface -- |t Acknowledgments -- |t I. Introduction and the general scheme -- |t II. Forcing relation and Aubry-Mather type -- |t III. Proving forcing equivalence -- |t IV. Supplementary topics -- |t Appendix: Notations -- |t References |
506 | 0 | |a restricted access |u http://purl.org/coar/access_right/c_16ec |f online access with authorization |2 star | |
520 | |a 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. | ||
538 | |a Mode of access: Internet via World Wide Web. | ||
546 | |a In English. | ||
588 | 0 | |a Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022) | |
650 | 0 | |a Diffusion |x Mathematical models. | |
650 | 0 | |a Hamiltonian systems. | |
650 | 7 | |a SCIENCE / Mechanics / Dynamics. |2 bisacsh | |
653 | |a Arnold's paper. | ||
653 | |a Hamiltonian system. | ||
653 | |a KAM theorem. | ||
653 | |a action variables. | ||
653 | |a autonomous Hamiltonian system. | ||
653 | |a celestial mechanics. | ||
653 | |a conservation of action variables. | ||
653 | |a instability of dynamical systems. | ||
653 | |a integrable Hamiltonian systems. | ||
653 | |a linearly stable. | ||
653 | |a magnetic fields. | ||
653 | |a motion of charged particles. | ||
653 | |a negligible friction. | ||
653 | |a non integrable. | ||
653 | |a perturb. | ||
653 | |a several degrees of freedom. | ||
653 | |a stable solution. | ||
700 | 1 | |a Zhang, Ke, |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t EBOOK PACKAGE COMPLETE 2020 English |z 9783110704716 |
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773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t EBOOK PACKAGE Physics, Chemistry, Mat.Sc, Geosc 2020 English |z 9783110704754 |
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773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t Princeton Annals of Mathematics eBook-Package 1940-2020 |z 9783110494914 |o ZDB-23-PMB |
773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t Princeton University Press Complete eBook-Package 2020 |z 9783110690088 |
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