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Measure and Capacity of Wandering Domains in Gevrey near-Integrable Exact Symplectic Systems. (Record no. 9057)

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001 - CONTROL NUMBER
control field EBC5725347
003 - CONTROL NUMBER IDENTIFIER
control field MiAaPQ
005 - DATE AND TIME OF LATEST TRANSACTION
control field 20240724113622.0
006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS
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007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION
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008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION
fixed length control field 240724s2018 xx o ||||0 eng d
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 9781470449537
Qualifying information (electronic bk.)
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
Canceled/invalid ISBN 9781470434922
035 ## - SYSTEM CONTROL NUMBER
System control number (MiAaPQ)EBC5725347
035 ## - SYSTEM CONTROL NUMBER
System control number (Au-PeEL)EBL5725347
035 ## - SYSTEM CONTROL NUMBER
System control number (OCoLC)1081116963
040 ## - CATALOGING SOURCE
Original cataloging agency MiAaPQ
Language of cataloging eng
Description conventions rda
-- pn
Transcribing agency MiAaPQ
Modifying agency MiAaPQ
050 #4 - LIBRARY OF CONGRESS CALL NUMBER
Classification number QA665 .L399 2019
082 0# - DEWEY DECIMAL CLASSIFICATION NUMBER
Classification number 516.36
100 1# - MAIN ENTRY--PERSONAL NAME
Personal name Lazzarini, Laurent.
245 10 - TITLE STATEMENT
Title Measure and Capacity of Wandering Domains in Gevrey near-Integrable Exact Symplectic Systems.
250 ## - EDITION STATEMENT
Edition statement 1st ed.
264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE
Place of production, publication, distribution, manufacture Providence :
Name of producer, publisher, distributor, manufacturer American Mathematical Society,
Date of production, publication, distribution, manufacture, or copyright notice 2018.
264 #4 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE
Date of production, publication, distribution, manufacture, or copyright notice ©2019.
300 ## - PHYSICAL DESCRIPTION
Extent 1 online resource (122 pages)
336 ## - CONTENT TYPE
Content type term text
Content type code txt
Source rdacontent
337 ## - MEDIA TYPE
Media type term computer
Media type code c
Source rdamedia
338 ## - CARRIER TYPE
Carrier type term online resource
Carrier type code cr
Source rdacarrier
490 1# - SERIES STATEMENT
Series statement Memoirs of the American Mathematical Society Series ;
Volume/sequential designation v.257
505 0# - FORMATTED CONTENTS NOTE
Formatted contents note Cover -- Title page -- Chapter 0. Introduction -- Chapter 1. Presentation of the results -- 1.1. Perturbation theory for analytic or Gevrey near-integrable maps-Theorem A -- 1.2. Wandering sets of near-integrable systems-Theorems B and C -- 1.3. Specific form of our examples and elliptic islands-Theorem D -- 1.4. Further comments -- Chapter 2. Stability theory for Gevrey near-integrable maps -- 2.1. Embedding in a Hamiltonian flow -Theorem E -- 2.2. Proof of Theorem E in the Gevrey non-analytic case -- 2.2.0. Overview -- 2.2.1. First step: finding a generating function -- 2.2.2. Second step: constructing a Hamiltonian isotopy -- 2.2.3. Completion of the proof of Theorem E -- 2.3. Proof of Theorem A (Nekhoroshev Theorem for maps) -- 2.4. Proof of Theorem B (upper bounds for wandering sets) -- Chapter 3. A quantitative KAM result-proof of Part (i) of Theorem D -- 3.1. Elliptic islands in \A with a tuning parameter-Theorem F -- 3.2. Theorem F implies Part (i) of Theorem D -- 3.3. Overview of the proof of Theorem F -- 3.4. Preliminary study near a q-periodic point -- 3.4.1. Localization -- 3.4.2. Local form -- 3.4.3. The Taylor expansion of the q iteration of G -- 3.5. Normalizations -- 3.5.1. Notations and statements -- Birkhoff normal form -- Herman normal form -- 3.5.2. Proof of Proposition 3.16 -- 3.5.3. Proof of Proposition 3.17 -- 3.5.4. Proof of Proposition 3.18 -- 3.6. The invariant curve theorem -- 3.7. Conclusion of the proof of Theorem F -- Chapter 4. Coupling devices, multi-dimensional periodic domains, wandering domains -- 4.1. Coupling devices -- 4.2. Proof of Part (ii) of Theorem D (periodic domains in \Aⁿ⁻¹) -- 4.2.1. Overview of the method -- 4.2.2. A -periodic polydisc for a near-integrable system of the form Φ^{ }∘ ^{ } in \A -- 4.2.3. A -periodic polydisc for a near-integrable system in \Aⁿ⁻² -- 4.2.4. Applying Corollary 4.2.
505 8# - FORMATTED CONTENTS NOTE
Formatted contents note 4.3. Proof of Theorem C (lower bounds for wandering domains in \Aⁿ) -- 4.3.1. Overview of the proof -- 4.3.2. Standard maps with wandering discs in \A -Proof of Proposition 4.6 -- 4.3.3. Proof of Theorem C' -- \appendixtocname -- Appendix A. Algebraic operations in O -- Appendix B. Estimates on Gevrey maps -- B.1. Reminder on Gevrey maps and their composition -- B.2. A lemma on the flow of a Gevrey near-integrable Hamiltonian -- B.3. Proof of Proposition 1.7 -- B.4. Gevrey bump fuctions -- Appendix C. Generating functions for exact symplectic ^{∞} maps -- Appendix D. Proof of Lemma 2.5 -- D.1. Set-up -- D.2. Diffeomorphism property -- D.3. Study of the inverse map -- Acknowledgements -- Bibliography -- Back Cover.
520 ## - SUMMARY, ETC.
Summary, etc. A wandering domain for a diffeomorphism \Psi of \mathbb A^n=T^*\mathbb T^n is an open connected set W such that \Psi ^k(W)\cap W=\emptyset for all k\in \mathbb Z^*. The authors endow \mathbb A^n with its usual exact symplectic structure. An integrable diffeomorphism, i.e., the time-one map \Phi ^h of a Hamiltonian h: \mathbb A^n\to \mathbb R which depends only on the action variables, has no nonempty wandering domains. The aim of this paper is to estimate the size (measure and Gromov capacity) of wandering domains in the case of an exact symplectic perturbation of \Phi ^h, in the analytic or Gevrey category. Upper estimates are related to Nekhoroshev theory; lower estimates are related to examples of Arnold diffusion. This is a contribution to the "quantitative Hamiltonian perturbation theory" initiated in previous works on the optimality of long term stability estimates and diffusion times; the emphasis here is on discrete systems because this is the natural setting to study wandering domains.
588 ## - SOURCE OF DESCRIPTION NOTE
Source of description note Description based on publisher supplied metadata and other sources.
590 ## - LOCAL NOTE (RLIN)
Local note Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name entry element Symplectic geometry.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name entry element Symplectic groups.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name entry element Domains of holomorphy.
655 #4 - INDEX TERM--GENRE/FORM
Genre/form data or focus term Electronic books.
700 1# - ADDED ENTRY--PERSONAL NAME
Personal name Marco, Jean-Pierre.
700 1# - ADDED ENTRY--PERSONAL NAME
Personal name Sauzin, David.
776 08 - ADDITIONAL PHYSICAL FORM ENTRY
Relationship information Print version:
Main entry heading Lazzarini, Laurent
Title Measure and Capacity of Wandering Domains in Gevrey near-Integrable Exact Symplectic Systems
Place, publisher, and date of publication Providence : American Mathematical Society,c2018
International Standard Book Number 9781470434922
797 2# - LOCAL ADDED ENTRY--CORPORATE NAME (RLIN)
Corporate name or jurisdiction name as entry element ProQuest (Firm)
830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE
Uniform title Memoirs of the American Mathematical Society Series
856 40 - ELECTRONIC LOCATION AND ACCESS
Uniform Resource Identifier <a href="https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=5725347">https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=5725347</a>
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