Reversible Hamiltonian Liapunov center theorem
Autor(a) principal: | |
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Data de Publicação: | 2005 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://www2.imperial.ac.uk/~jswlamb/papers/Buzzi_Lamb51_66.pdf http://hdl.handle.net/11449/68120 |
Resumo: | We study the existence of periodic solutions in the neighbourhood of symmetric (partially) elliptic equilibria in purely reversible Hamiltonian vector fields. These are Hamiltonian vector fields with an involutory reversing symmetry R. We contrast the cases where R acts symplectically and anti-symplectically. In case R acts anti-symplectically, generically purely imaginary eigenvalues are isolated, and the equilibrium is contained in a local two-dimensional invariant manifold containing symmetric periodic solutions encircling the equilibrium point. In case R acts symplectically, generically purely imaginary eigenvalues are doubly degenerate, and the equilibrium is contained in two two-dimensional invariant manifolds containing nonsymmetric periodic solutions encircling the equilibrium point. In addition, there exists a three-dimensional invariant surface containing a two-parameter family of symmetric periodic solutions. |
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Repositório Institucional da UNESP |
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Reversible Hamiltonian Liapunov center theoremLiapunov center theoremTime-reversal symmetryWe study the existence of periodic solutions in the neighbourhood of symmetric (partially) elliptic equilibria in purely reversible Hamiltonian vector fields. These are Hamiltonian vector fields with an involutory reversing symmetry R. We contrast the cases where R acts symplectically and anti-symplectically. In case R acts anti-symplectically, generically purely imaginary eigenvalues are isolated, and the equilibrium is contained in a local two-dimensional invariant manifold containing symmetric periodic solutions encircling the equilibrium point. In case R acts symplectically, generically purely imaginary eigenvalues are doubly degenerate, and the equilibrium is contained in two two-dimensional invariant manifolds containing nonsymmetric periodic solutions encircling the equilibrium point. In addition, there exists a three-dimensional invariant surface containing a two-parameter family of symmetric periodic solutions.IBILCE UNESP, Sao Jose do Rio Preto, CEP 15054-000Department of Mathematics Imperial College London, London SW7 2AZIBILCE UNESP, Sao Jose do Rio Preto, CEP 15054-000Universidade Estadual Paulista (Unesp)Imperial College LondonBuzzi, Claudio A. [UNESP]Lamb, Jeroen S.W.2014-05-27T11:21:16Z2014-05-27T11:21:16Z2005-02-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article51-66application/pdfhttp://www2.imperial.ac.uk/~jswlamb/papers/Buzzi_Lamb51_66.pdfDiscrete and Continuous Dynamical Systems - Series B, v. 5, n. 1, p. 51-66, 2005.1531-3492http://hdl.handle.net/11449/68120WOS:0002267418000052-s2.0-158444099372-s2.0-15844409937.pdf66828677607174450000-0003-2037-8417Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengDiscrete and Continuous Dynamical Systems: Series B0.9720,864info:eu-repo/semantics/openAccess2024-01-10T06:28:45Zoai:repositorio.unesp.br:11449/68120Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-01-10T06:28:45Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Reversible Hamiltonian Liapunov center theorem |
title |
Reversible Hamiltonian Liapunov center theorem |
spellingShingle |
Reversible Hamiltonian Liapunov center theorem Buzzi, Claudio A. [UNESP] Liapunov center theorem Time-reversal symmetry |
title_short |
Reversible Hamiltonian Liapunov center theorem |
title_full |
Reversible Hamiltonian Liapunov center theorem |
title_fullStr |
Reversible Hamiltonian Liapunov center theorem |
title_full_unstemmed |
Reversible Hamiltonian Liapunov center theorem |
title_sort |
Reversible Hamiltonian Liapunov center theorem |
author |
Buzzi, Claudio A. [UNESP] |
author_facet |
Buzzi, Claudio A. [UNESP] Lamb, Jeroen S.W. |
author_role |
author |
author2 |
Lamb, Jeroen S.W. |
author2_role |
author |
dc.contributor.none.fl_str_mv |
Universidade Estadual Paulista (Unesp) Imperial College London |
dc.contributor.author.fl_str_mv |
Buzzi, Claudio A. [UNESP] Lamb, Jeroen S.W. |
dc.subject.por.fl_str_mv |
Liapunov center theorem Time-reversal symmetry |
topic |
Liapunov center theorem Time-reversal symmetry |
description |
We study the existence of periodic solutions in the neighbourhood of symmetric (partially) elliptic equilibria in purely reversible Hamiltonian vector fields. These are Hamiltonian vector fields with an involutory reversing symmetry R. We contrast the cases where R acts symplectically and anti-symplectically. In case R acts anti-symplectically, generically purely imaginary eigenvalues are isolated, and the equilibrium is contained in a local two-dimensional invariant manifold containing symmetric periodic solutions encircling the equilibrium point. In case R acts symplectically, generically purely imaginary eigenvalues are doubly degenerate, and the equilibrium is contained in two two-dimensional invariant manifolds containing nonsymmetric periodic solutions encircling the equilibrium point. In addition, there exists a three-dimensional invariant surface containing a two-parameter family of symmetric periodic solutions. |
publishDate |
2005 |
dc.date.none.fl_str_mv |
2005-02-01 2014-05-27T11:21:16Z 2014-05-27T11:21:16Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://www2.imperial.ac.uk/~jswlamb/papers/Buzzi_Lamb51_66.pdf Discrete and Continuous Dynamical Systems - Series B, v. 5, n. 1, p. 51-66, 2005. 1531-3492 http://hdl.handle.net/11449/68120 WOS:000226741800005 2-s2.0-15844409937 2-s2.0-15844409937.pdf 6682867760717445 0000-0003-2037-8417 |
url |
http://www2.imperial.ac.uk/~jswlamb/papers/Buzzi_Lamb51_66.pdf http://hdl.handle.net/11449/68120 |
identifier_str_mv |
Discrete and Continuous Dynamical Systems - Series B, v. 5, n. 1, p. 51-66, 2005. 1531-3492 WOS:000226741800005 2-s2.0-15844409937 2-s2.0-15844409937.pdf 6682867760717445 0000-0003-2037-8417 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Discrete and Continuous Dynamical Systems: Series B 0.972 0,864 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
51-66 application/pdf |
dc.source.none.fl_str_mv |
Scopus reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
|
_version_ |
1803047311119482880 |