KAM theorem for Gevrey Hamiltonians
Identifieur interne : 001268 ( Istex/Corpus ); précédent : 001267; suivant : 001269KAM theorem for Gevrey Hamiltonians
Auteurs : G. PopovSource :
- Ergodic Theory and Dynamical Systems [ 0143-3857 ] ; 2004-10.
Abstract
We consider Gevrey perturbations H of a completely integrable non-degenerate Gevrey Hamiltonian H 0. Given a Cantor set $\Omega_\kappa$ defined by a Diophantine condition, we find a family of Kolmogorov–Arnold–Moser (KAM) invariant tori of H with frequencies $\omega\in \Omega_\kappa$ which is Gevrey smooth in a Whitney sense. Moreover, we obtain a symplectic Gevrey normal form of the Hamiltonian in a neighborhood of the union $\Lambda$ of the invariant tori. This leads to effective stability of the quasi-periodic motion near $\Lambda$.
Url:
DOI: 10.1017/S0143385704000458
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This leads to effective stability of the quasi-periodic motion near $\Lambda$.</p></abstract></profileDesc><revisionDesc><change when="2004-10-18">Created</change><change when="2004-10">Published</change></revisionDesc></teiHeader></istex:fulltextTEI><json:item><extension>txt</extension><original>false</original><mimetype>text/plain</mimetype><uri>https://api.istex.fr/ark:/67375/6GQ-9GWVFRVM-7/fulltext.txt</uri></json:item></fulltext><metadata><istex:metadataXml wicri:clean="corpus cambridge not found" wicri:toSee="no header"><istex:xmlDeclaration>version='1.0' encoding='UTF-8'</istex:xmlDeclaration><istex:docType PUBLIC="-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.0 20120330//EN" URI="JATS-journalpublishing1.dtd" name="istex:docType"></istex:docType><istex:document><article dtd-version="1.0" article-type="research-article"><front><journal-meta><journal-id journal-id-type="publisher-id">ETS</journal-id><journal-title-group><journal-title>Ergodic Theory and Dynamical Systems</journal-title><abbrev-journal-title>Ergod. Th. Dynam. Sys.</abbrev-journal-title></journal-title-group><issn pub-type="epub">1469-4417</issn><issn pub-type="ppub">0143-3857</issn><publisher><publisher-name>Cambridge University Press</publisher-name><publisher-loc>Cambridge, UK</publisher-loc></publisher></journal-meta><article-meta><article-id pub-id-type="pii">S0143385704000458</article-id><article-id pub-id-type="doi">10.1017/S0143385704000458</article-id><title-group><article-title>KAM theorem for Gevrey Hamiltonians</article-title></title-group><contrib-group><contrib><name><surname>POPOV</surname><given-names>G.</given-names></name><aff><institution>Université de Nantes</institution>, Département de Mathématiques, UMR 6629 du CNRS, 2, rue de la Houssinière, BP 92208, 44072 Nantes Cedex 03, <country>France</country> (e-mail: <email>popov@math.univ-nantes.fr</email>)</aff></contrib></contrib-group><pub-date pub-type="epub"><day>18</day><month>10</month><year>2004</year></pub-date><pub-date pub-type="ppub"><month>10</month><year>2004</year></pub-date><volume>24</volume><issue>5</issue><fpage>1753</fpage><lpage>1786</lpage><history><date date-type="accepted"><day>29</day><month>3</month><year>2004</year></date><date date-type="received"><day>2</day><month>4</month><year>2003</year></date></history><permissions><copyright-statement>© 2004 Cambridge University Press</copyright-statement></permissions><abstract abstract-type="normal"><p>We consider Gevrey perturbations <italic>H</italic> of a completely integrable non-degenerate Gevrey Hamiltonian <italic>H</italic><sup>0</sup>. Given a Cantor set <inline-formula id="ffm001">$\Omega_\kappa$</inline-formula> defined by a Diophantine condition, we find a family of Kolmogorov–Arnold–Moser (KAM) invariant tori of <italic>H</italic> with frequencies <inline-formula id="ffm002">$\omega\in \Omega_\kappa$</inline-formula> which is Gevrey smooth in a Whitney sense. Moreover, we obtain a symplectic Gevrey normal form of the Hamiltonian in a neighborhood of the union <inline-formula id="ffm003">$\Lambda$</inline-formula> of the invariant tori. This leads to effective stability of the quasi-periodic motion near <inline-formula id="ffm004">$\Lambda$</inline-formula>.</p></abstract><counts><page-count count="34"></page-count></counts><custom-meta-group><custom-meta><meta-name>pdf</meta-name><meta-value>S0143385704000458a.pdf</meta-value></custom-meta></custom-meta-group></article-meta></front></article></istex:document></istex:metadataXml><mods version="3.6"><titleInfo><title>KAM theorem for Gevrey Hamiltonians</title></titleInfo><titleInfo type="alternative" contentType="CDATA"><title>KAM theorem for Gevrey Hamiltonians</title></titleInfo><name type="personal"><namePart type="given">G.</namePart><namePart type="family">POPOV</namePart><affiliation>Université de Nantes</affiliation><affiliation>E-mail: popov@math.univ-nantes.fr</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="research-article" displayLabel="research-article" authority="ISTEX" authorityURI="https://content-type.data.istex.fr" valueURI="https://content-type.data.istex.fr/ark:/67375/XTP-1JC4F85T-7">research-article</genre><originInfo><publisher>Cambridge University Press</publisher><place><placeTerm type="text">Cambridge, UK</placeTerm></place><dateIssued encoding="w3cdtf">2004-10</dateIssued><dateCreated encoding="w3cdtf">2004-10-18</dateCreated><copyrightDate encoding="w3cdtf">2004</copyrightDate></originInfo><language><languageTerm type="code" authority="iso639-2b">eng</languageTerm><languageTerm type="code" authority="rfc3066">en</languageTerm></language><abstract type="normal">We consider Gevrey perturbations H of a completely integrable non-degenerate Gevrey Hamiltonian H 0. Given a Cantor set $\Omega_\kappa$ defined by a Diophantine condition, we find a family of Kolmogorov–Arnold–Moser (KAM) invariant tori of H with frequencies $\omega\in \Omega_\kappa$ which is Gevrey smooth in a Whitney sense. Moreover, we obtain a symplectic Gevrey normal form of the Hamiltonian in a neighborhood of the union $\Lambda$ of the invariant tori. 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