The parameterization method for invariant manifolds III: overview and applications

We describe a method to establish existence and regularity of invariant manifolds and, at the same time to find simple maps which are conjugated to the dynamics on them. The method establishes several invariant manifold theorems. For instance, it reduces the proof of the usual stable manifold theore...

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Authors: Cabré Vilagut, Xavier|||0000-0001-5682-3135, Fontich i Julià, Ernest, Llave Canosa, Rafael de la
Format: article
Publication Date:2003
Country:España
Institution:Universitat Politècnica de Catalunya (UPC)
Repository:UPCommons. Portal del coneixement obert de la UPC
Language:English
OAI Identifier:oai:upcommons.upc.edu:2117/910
Online Access:https://hdl.handle.net/2117/910
Access Level:Open access
Keyword:Differentiable dynamical systems
invariant manifolds
Sistemes dinàmics diferenciables
Teoria ergòdica
Classificació AMS::37 Dynamical systems and ergodic theory::37D Dynamical systems with hyperbolic behavior
Classificació AMS::37 Dynamical systems and ergodic theory::37M Approximation methods and numerical treatment of dynamical systems
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spelling The parameterization method for invariant manifolds III: overview and applicationsCabré Vilagut, Xavier|||0000-0001-5682-3135Fontich i Julià, ErnestLlave Canosa, Rafael de laDifferentiable dynamical systemsinvariant manifoldsSistemes dinàmics diferenciablesTeoria ergòdicaClassificació AMS::37 Dynamical systems and ergodic theory::37D Dynamical systems with hyperbolic behaviorClassificació AMS::37 Dynamical systems and ergodic theory::37M Approximation methods and numerical treatment of dynamical systemsWe describe a method to establish existence and regularity of invariant manifolds and, at the same time to find simple maps which are conjugated to the dynamics on them. The method establishes several invariant manifold theorems. For instance, it reduces the proof of the usual stable manifold theorem near hyperbolic points to an application of the implicit function theorem in Banach spaces. We also present several other applications of the method.20032003-01-0120072007-05-07journal articlehttp://purl.org/coar/resource_type/c_6501NAhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/910reponame: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:2117/9102026-05-27T15:37:01Z
dc.title.none.fl_str_mv The parameterization method for invariant manifolds III: overview and applications
title The parameterization method for invariant manifolds III: overview and applications
spellingShingle The parameterization method for invariant manifolds III: overview and applications
Cabré Vilagut, Xavier|||0000-0001-5682-3135
Differentiable dynamical systems
invariant manifolds
Sistemes dinàmics diferenciables
Teoria ergòdica
Classificació AMS::37 Dynamical systems and ergodic theory::37D Dynamical systems with hyperbolic behavior
Classificació AMS::37 Dynamical systems and ergodic theory::37M Approximation methods and numerical treatment of dynamical systems
title_short The parameterization method for invariant manifolds III: overview and applications
title_full The parameterization method for invariant manifolds III: overview and applications
title_fullStr The parameterization method for invariant manifolds III: overview and applications
title_full_unstemmed The parameterization method for invariant manifolds III: overview and applications
title_sort The parameterization method for invariant manifolds III: overview and applications
dc.creator.none.fl_str_mv Cabré Vilagut, Xavier|||0000-0001-5682-3135
Fontich i Julià, Ernest
Llave Canosa, Rafael de la
author Cabré Vilagut, Xavier|||0000-0001-5682-3135
author_facet Cabré Vilagut, Xavier|||0000-0001-5682-3135
Fontich i Julià, Ernest
Llave Canosa, Rafael de la
author_role author
author2 Fontich i Julià, Ernest
Llave Canosa, Rafael de la
author2_role author
author
dc.subject.none.fl_str_mv Differentiable dynamical systems
invariant manifolds
Sistemes dinàmics diferenciables
Teoria ergòdica
Classificació AMS::37 Dynamical systems and ergodic theory::37D Dynamical systems with hyperbolic behavior
Classificació AMS::37 Dynamical systems and ergodic theory::37M Approximation methods and numerical treatment of dynamical systems
topic Differentiable dynamical systems
invariant manifolds
Sistemes dinàmics diferenciables
Teoria ergòdica
Classificació AMS::37 Dynamical systems and ergodic theory::37D Dynamical systems with hyperbolic behavior
Classificació AMS::37 Dynamical systems and ergodic theory::37M Approximation methods and numerical treatment of dynamical systems
description We describe a method to establish existence and regularity of invariant manifolds and, at the same time to find simple maps which are conjugated to the dynamics on them. The method establishes several invariant manifold theorems. For instance, it reduces the proof of the usual stable manifold theorem near hyperbolic points to an application of the implicit function theorem in Banach spaces. We also present several other applications of the method.
publishDate 2003
dc.date.none.fl_str_mv 2003
2003-01-01
2007
2007-05-07
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/2117/910
url https://hdl.handle.net/2117/910
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)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869415780026679296
score 15,301603

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