KAM theory and a partial justification of Greene's criterion for non-twist maps
We consider perturbations of integrable area preserving non twist maps of the annulus those are maps in which the twist condition changes sign These maps appear in a variety of applications notably transport in atmospheric Rossby waves We show in suitable parameter families the persistence of critic...
| Autores: | , |
|---|---|
| Formato: | artículo |
| Fecha de publicación: | 1999 |
| País: | España |
| Recursos: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/1191 |
| Acesso em linha: | https://hdl.handle.net/2117/1191 |
| Access Level: | acceso abierto |
| Palavra-chave: | Hamiltonian dynamical systems Lagrangian functions Differentiable dynamical systems Hamiltonian systems Greene's criterion KAM theory Hamilton, Sistemes de Lagrange, Funcions de Sistemes dinàmics diferenciables Classificació AMS::37 Dynamical systems and ergodic theory::37E Low-dimensional dynamical systems Classificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems Classificació AMS::70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics |
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KAM theory and a partial justification of Greene's criterion for non-twist mapsDelshams Valdés, Amadeu|||0000-0003-4134-8882Llave Canosa, Rafael de laHamiltonian dynamical systemsLagrangian functionsDifferentiable dynamical systemsHamiltonian systemsGreene's criterionKAM theoryHamilton, Sistemes deLagrange, Funcions deSistemes dinàmics diferenciablesClassificació AMS::37 Dynamical systems and ergodic theory::37E Low-dimensional dynamical systemsClassificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systemsClassificació AMS::70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanicsWe consider perturbations of integrable area preserving non twist maps of the annulus those are maps in which the twist condition changes sign These maps appear in a variety of applications notably transport in atmospheric Rossby waves We show in suitable parameter families the persistence of critical circles invariant circles whose rotation number is the maximum of all the rotation numbers of points in the map with Diophantine rotation number The parameter values with critical circles of frequency lie on a one dimensional analytic curve Furthermore we show a partial justication of Greenes criterion If analytic critical curves with Dio phantine rotation number exist the residue of periodic orbits that is one fourth of the trace of the derivative of the return map minus with rotation number converging to converges to zero exponen tially fast We also show that if analytic curves exist there should be periodic orbits approximating them and indicate how to compute them These results justify in particular conjectures put forward on the basis of numerical evidence in D del Castillo et al Phys D The proof of both results relies on the successive application of an iterative lemma which is valid also for d dimensional exact symplectic di eomorphisms The proof of this iterative lemma is based on the deformation method of singularity theory19991999-01-0120072007-09-28journal articlehttp://purl.org/coar/resource_type/c_6501NAhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/1191reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivs 2.5 Spainhttp://creativecommons.org/licenses/by-nc-nd/2.5/es/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/11912026-05-27T15:37:01Z |
| dc.title.none.fl_str_mv |
KAM theory and a partial justification of Greene's criterion for non-twist maps |
| title |
KAM theory and a partial justification of Greene's criterion for non-twist maps |
| spellingShingle |
KAM theory and a partial justification of Greene's criterion for non-twist maps Delshams Valdés, Amadeu|||0000-0003-4134-8882 Hamiltonian dynamical systems Lagrangian functions Differentiable dynamical systems Hamiltonian systems Greene's criterion KAM theory Hamilton, Sistemes de Lagrange, Funcions de Sistemes dinàmics diferenciables Classificació AMS::37 Dynamical systems and ergodic theory::37E Low-dimensional dynamical systems Classificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems Classificació AMS::70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics |
| title_short |
KAM theory and a partial justification of Greene's criterion for non-twist maps |
| title_full |
KAM theory and a partial justification of Greene's criterion for non-twist maps |
| title_fullStr |
KAM theory and a partial justification of Greene's criterion for non-twist maps |
| title_full_unstemmed |
KAM theory and a partial justification of Greene's criterion for non-twist maps |
| title_sort |
KAM theory and a partial justification of Greene's criterion for non-twist maps |
| dc.creator.none.fl_str_mv |
Delshams Valdés, Amadeu|||0000-0003-4134-8882 Llave Canosa, Rafael de la |
| author |
Delshams Valdés, Amadeu|||0000-0003-4134-8882 |
| author_facet |
Delshams Valdés, Amadeu|||0000-0003-4134-8882 Llave Canosa, Rafael de la |
| author_role |
author |
| author2 |
Llave Canosa, Rafael de la |
| author2_role |
author |
| dc.subject.none.fl_str_mv |
Hamiltonian dynamical systems Lagrangian functions Differentiable dynamical systems Hamiltonian systems Greene's criterion KAM theory Hamilton, Sistemes de Lagrange, Funcions de Sistemes dinàmics diferenciables Classificació AMS::37 Dynamical systems and ergodic theory::37E Low-dimensional dynamical systems Classificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems Classificació AMS::70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics |
| topic |
Hamiltonian dynamical systems Lagrangian functions Differentiable dynamical systems Hamiltonian systems Greene's criterion KAM theory Hamilton, Sistemes de Lagrange, Funcions de Sistemes dinàmics diferenciables Classificació AMS::37 Dynamical systems and ergodic theory::37E Low-dimensional dynamical systems Classificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems Classificació AMS::70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics |
| description |
We consider perturbations of integrable area preserving non twist maps of the annulus those are maps in which the twist condition changes sign These maps appear in a variety of applications notably transport in atmospheric Rossby waves We show in suitable parameter families the persistence of critical circles invariant circles whose rotation number is the maximum of all the rotation numbers of points in the map with Diophantine rotation number The parameter values with critical circles of frequency lie on a one dimensional analytic curve Furthermore we show a partial justication of Greenes criterion If analytic critical curves with Dio phantine rotation number exist the residue of periodic orbits that is one fourth of the trace of the derivative of the return map minus with rotation number converging to converges to zero exponen tially fast We also show that if analytic curves exist there should be periodic orbits approximating them and indicate how to compute them These results justify in particular conjectures put forward on the basis of numerical evidence in D del Castillo et al Phys D The proof of both results relies on the successive application of an iterative lemma which is valid also for d dimensional exact symplectic di eomorphisms The proof of this iterative lemma is based on the deformation method of singularity theory |
| publishDate |
1999 |
| dc.date.none.fl_str_mv |
1999 1999-01-01 2007 2007-09-28 |
| dc.type.none.fl_str_mv |
journal article http://purl.org/coar/resource_type/c_6501 NA http://purl.org/coar/version/c_be7fb7dd8ff6fe43 |
| dc.type.openaire.fl_str_mv |
info:eu-repo/semantics/article |
| format |
article |
| dc.identifier.none.fl_str_mv |
https://hdl.handle.net/2117/1191 |
| url |
https://hdl.handle.net/2117/1191 |
| dc.language.none.fl_str_mv |
Inglés eng |
| language_invalid_str_mv |
Inglés |
| language |
eng |
| dc.rights.none.fl_str_mv |
open access http://purl.org/coar/access_right/c_abf2 Attribution-NonCommercial-NoDerivs 2.5 Spain http://creativecommons.org/licenses/by-nc-nd/2.5/es/ |
| dc.rights.openaire.fl_str_mv |
info:eu-repo/semantics/openAccess |
| rights_invalid_str_mv |
open access http://purl.org/coar/access_right/c_abf2 Attribution-NonCommercial-NoDerivs 2.5 Spain http://creativecommons.org/licenses/by-nc-nd/2.5/es/ |
| eu_rights_str_mv |
openAccess |
| dc.format.none.fl_str_mv |
application/pdf |
| dc.source.none.fl_str_mv |
reponame:UPCommons. Portal del coneixement obert de la UPC instname:Universitat Politècnica de Catalunya (UPC) |
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Universitat Politècnica de Catalunya (UPC) |
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UPCommons. Portal del coneixement obert de la UPC |
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UPCommons. Portal del coneixement obert de la UPC |
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| repository.mail.fl_str_mv |
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1869423909185519616 |
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15.300719 |