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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Place / Publishing House: | Princeton, NJ : : Princeton University Press, , [2020] ©2020 |
Year of Publication: | 2020 |
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Series: | Annals of Mathematics Studies ;
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Kaloshin, Vadim, author. aut http://id.loc.gov/vocabulary/relators/aut Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom : (AMS-208) / Ke Zhang, Vadim Kaloshin. Princeton, NJ : Princeton University Press, [2020] ©2020 1 online resource (224 p.) : 21 b/w illus. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Annals of Mathematics Studies ; 384 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 restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star 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. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022) Diffusion Mathematical models. Hamiltonian systems. SCIENCE / Mechanics / Dynamics. bisacsh 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. Zhang, Ke, author. aut http://id.loc.gov/vocabulary/relators/aut Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2020 English 9783110704716 Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2020 9783110704518 ZDB-23-DGG Title is part of eBook package: De Gruyter EBOOK PACKAGE Physics, Chemistry, Mat.Sc, Geosc 2020 English 9783110704754 Title is part of eBook package: De Gruyter EBOOK PACKAGE Physics, Chemistry, Mat.Sc, Geosc 2020 9783110704556 ZDB-23-DPC Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 9783110494914 ZDB-23-PMB Title is part of eBook package: De Gruyter Princeton University Press Complete eBook-Package 2020 9783110690088 https://doi.org/10.1515/9780691204932?locatt=mode:legacy https://www.degruyter.com/isbn/9780691204932 Cover https://www.degruyter.com/document/cover/isbn/9780691204932/original |
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Kaloshin, Vadim, Kaloshin, Vadim, Zhang, Ke, |
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Kaloshin, Vadim, Kaloshin, Vadim, Zhang, Ke, Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom : (AMS-208) / Annals of Mathematics Studies ; 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 |
author_facet |
Kaloshin, Vadim, Kaloshin, Vadim, Zhang, Ke, Zhang, Ke, Zhang, Ke, |
author_variant |
v k vk v k vk k z kz |
author_role |
VerfasserIn VerfasserIn VerfasserIn |
author2 |
Zhang, Ke, Zhang, Ke, |
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k z kz |
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author_sort |
Kaloshin, Vadim, |
title |
Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom : (AMS-208) / |
title_sub |
(AMS-208) / |
title_full |
Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom : (AMS-208) / Ke Zhang, Vadim Kaloshin. |
title_fullStr |
Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom : (AMS-208) / Ke Zhang, Vadim Kaloshin. |
title_full_unstemmed |
Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom : (AMS-208) / Ke Zhang, Vadim Kaloshin. |
title_auth |
Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom : (AMS-208) / |
title_alt |
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 |
title_new |
Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom : |
title_sort |
arnold diffusion for smooth systems of two and a half degrees of freedom : (ams-208) / |
series |
Annals of Mathematics Studies ; |
series2 |
Annals of Mathematics Studies ; |
publisher |
Princeton University Press, |
publishDate |
2020 |
physical |
1 online resource (224 p.) : 21 b/w illus. |
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 |
isbn |
9780691204932 9783110704716 9783110704518 9783110704754 9783110704556 9783110494914 9783110690088 |
callnumber-first |
Q - Science |
callnumber-subject |
QA - Mathematics |
callnumber-label |
QA614 |
callnumber-sort |
QA 3614.83 K35 42020EB |
url |
https://doi.org/10.1515/9780691204932?locatt=mode:legacy https://www.degruyter.com/isbn/9780691204932 https://www.degruyter.com/document/cover/isbn/9780691204932/original |
illustrated |
Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
510 - Mathematics |
dewey-ones |
514 - Topology |
dewey-full |
514.74 |
dewey-sort |
3514.74 |
dewey-raw |
514.74 |
dewey-search |
514.74 |
doi_str_mv |
10.1515/9780691204932?locatt=mode:legacy |
oclc_num |
1202461041 |
work_keys_str_mv |
AT kaloshinvadim arnolddiffusionforsmoothsystemsoftwoandahalfdegreesoffreedomams208 AT zhangke arnolddiffusionforsmoothsystemsoftwoandahalfdegreesoffreedomams208 |
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ids_txt_mv |
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Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2020 English Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2020 Title is part of eBook package: De Gruyter EBOOK PACKAGE Physics, Chemistry, Mat.Sc, Geosc 2020 English Title is part of eBook package: De Gruyter EBOOK PACKAGE Physics, Chemistry, Mat.Sc, Geosc 2020 Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 Title is part of eBook package: De Gruyter Princeton University Press Complete eBook-Package 2020 |
is_hierarchy_title |
Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom : (AMS-208) / |
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Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2020 English |
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