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Introduction to Arnold's proof of the Kolmogorov-Arnold-Moser theorem /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Introduction to Arnold's proof of the Kolmogorov-Arnold-Moser theorem /Achim Feldmeier.
作者:	Feldmeier, Achim,
出版者:	Boca Raton :CRC Press,2023.
面頁冊數:	xi, 205 p. :ill. ;24 cm.
標題:	Kolmogorov-Arnold-Moser theory.
ISBN:	9781032260655 (hbk.) :

Introduction to Arnold's proof of the Kolmogorov-Arnold-Moser theorem /
Feldmeier, Achim,

Introduction to Arnold's proof of the Kolmogorov-Arnold-Moser theorem /Achim Feldmeier. - 1st ed. - Boca Raton :CRC Press,2023. - xi, 205 p. :ill. ;24 cm.

Includes bibliographical references and index.

Hamilton theory -- Preliminaries -- Outline of the KAM proof -- Proof of the KAM theorem -- Analytic lemmas -- Geometric lemmas -- Convergence lemmas -- Arithmetic lemmas.

"This book provides an accessible step-by-step account of Arnold's classical proof of the Kolmogorov-Arnold-Moser (KAM) Theorem. It begins with a general background of the theorem and proves the famous Liouville-Arnold theorem for integrable systems and introduces Kneser's tori in four-dimensional phase space. It then introduces and discusses the ideas and techniques used in Arnold's proof, before the second half of the book walks the reader through a detailed account of Arnold's proof with all the required steps. It will be a useful guide for advanced students of mathematical physics, in addition to researchers and professionals. Key features: Applies concepts and theorems from real and complex analysis (e.g. Fourier series; implicit function theorem) and topology in the framework of this key theorem from mathematical physics. Covers all aspects of Arnold's proof, including those often left out in more general or simplified presentations. Discusses, in detail, the ideas used in the proof of the KAM theorem and puts them in historical context (e.g. mapping degree from algebraic topology)"--

ISBN: 9781032260655 (hbk.) :NT$5603

LCCN: 2022000886Subjects--Personal Names:

968082
Arnolʹd, V. I.
1937-2010.Subjects--Topical Terms:

968083
Kolmogorov-Arnold-Moser theory.

LC Class. No.: Q172.5.C45 / F45 2023

Dewey Class. No.: 530.15/539

Introduction to Arnold's proof of the Kolmogorov-Arnold-Moser theorem /
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008 240807s2023 flua b 001 0 eng
010 $a 2022000886
020 $a 9781032260655 (hbk.) : $c NT$5603
020 $a 1032260653 (hbk.)
020 $a 9781032263380 (pbk.)
020 $a 1032263385 (pbk.)
020 $z 9781003287803 (ebook)
020 $z 9781000610000 (ePub ebook)
020 $z 9781000609974 (PDF ebook)
035 $a (OCoLC)1292471044 $z (OCoLC)1292350587 $z (OCoLC)1292429087
035 $a on1292471044
040 $a LBSOR/DLC $b eng $c DLC $d BDX $d UKMGB $d YDX $d OCLCF $d OCLCO $d OCLCL
042 $a pcc
050 0 0 $a Q172.5.C45 $b F45 2023
082 0 0 $a 530.15/539
100 1 $a Feldmeier, Achim, $e author. $3 968081
245 1 0 $a Introduction to Arnold's proof of the Kolmogorov-Arnold-Moser theorem / $c Achim Feldmeier.
250 $a 1st ed.
260 $a Boca Raton : $b CRC Press, $c 2023.
300 $a xi, 205 p. : $b ill. ; $c 24 cm.
504 $a Includes bibliographical references and index.
505 0 $a Hamilton theory -- Preliminaries -- Outline of the KAM proof -- Proof of the KAM theorem -- Analytic lemmas -- Geometric lemmas -- Convergence lemmas -- Arithmetic lemmas.
520 $a "This book provides an accessible step-by-step account of Arnold's classical proof of the Kolmogorov-Arnold-Moser (KAM) Theorem. It begins with a general background of the theorem and proves the famous Liouville-Arnold theorem for integrable systems and introduces Kneser's tori in four-dimensional phase space. It then introduces and discusses the ideas and techniques used in Arnold's proof, before the second half of the book walks the reader through a detailed account of Arnold's proof with all the required steps. It will be a useful guide for advanced students of mathematical physics, in addition to researchers and professionals. Key features: Applies concepts and theorems from real and complex analysis (e.g. Fourier series; implicit function theorem) and topology in the framework of this key theorem from mathematical physics. Covers all aspects of Arnold's proof, including those often left out in more general or simplified presentations. Discusses, in detail, the ideas used in the proof of the KAM theorem and puts them in historical context (e.g. mapping degree from algebraic topology)"-- $c Provided by publisher.
600 1 0 $a Arnolʹd, V. I. $q (Vladimir Igorevich), $d 1937-2010. $3 968082
650 0 $a Kolmogorov-Arnold-Moser theory. $3 968083
650 0 $a Proof theory. $3 190840