Contribution to the study of invariant manifolds and the splitting of separatrices of parabolic points

[eng] In general, when beginning to explore any scientific field, one focuses on the generic situations; that is, one centers on the behaviours that appear in “most” of the cases encountered in practice. This methodology allows an easier understanding of the problem, since the non-generic (or degene...

ver descrição completa

Detalhes bibliográficos
Autor: Baldomá, Inmaculada
Formato: tesis doctoral
Estado:Versión publicada
Fecha de publicación:2001
País:España
Recursos:Universidad de Barcelona
Repositorio:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu:2445/182873
Acesso em linha:https://hdl.handle.net/2445/182873
http://hdl.handle.net/10803/673362
Access Level:acceso abierto
Palavra-chave:Varietats diferenciables
Sistemes dinàmics diferenciables
Sistemes hamiltonians
Differentiable manifolds
Differentiable dynamical systems
Hamiltonian systems
id ES_4e1259f3e4747abdd22d4cbef4076418
oai_identifier_str oai:diposit.ub.edu:2445/182873
network_acronym_str ES
network_name_str España
repository_id_str
spelling Contribution to the study of invariant manifolds and the splitting of separatrices of parabolic pointsBaldomá, InmaculadaVarietats diferenciablesSistemes dinàmics diferenciablesSistemes hamiltoniansDifferentiable manifoldsDifferentiable dynamical systemsHamiltonian systems[eng] In general, when beginning to explore any scientific field, one focuses on the generic situations; that is, one centers on the behaviours that appear in “most” of the cases encountered in practice. This methodology allows an easier understanding of the problem, since the non-generic (or degenerate) cases are left out (at least a priori) in a first approach. This way, the casuistic is simpler and the general theory can be developed more easily. Although this is a good scientific procedure, the aim of Science is to explain reality in the most complete way possible. So, when the general case has been already described (perhaps not completely, but at least in a good part), one should study the non-generic cases: the exceptions. It should not be forgotten that, in nature, not all the processes follow a general rule. The exceptional cases often provide new types of behaviour. Therefore, a lot can be learned from the exceptions, as much at an intrinsic level (situations that differ from the general qualitative behaviour) as for the new techniques that are developed in order to understand them. In certain contexts, it is generic to encounter degenerate cases. Let us think, for instance, about the case of parametric families, f(mi), which describe different behaviours depending on the value of mi. In this situation, it is generic (that is, it occurs in most of the families) to find values of the parameter f(mi)(0) for which the behaviour of f(mi)(0) is degenerate.Universitat de BarcelonaFontich, Ernest, 1955-Universitat de Barcelona. Departament de Matemàtica Aplicada i Anàlisi2001info:eu-repo/semantics/doctoralThesisinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://hdl.handle.net/2445/182873http://hdl.handle.net/10803/673362Tesis Doctorals - Departament - Matemàtica Aplicada i Anàlisireponame:Dipòsit Digital de la UBinstname:Universidad de BarcelonaIngléscc by-nc-sa (c) Baldomá, Inmaculada, 2022http://creativecommons.org/licenses/by-nc-sa/3.0/es/info:eu-repo/semantics/openAccessoai:diposit.ub.edu:2445/1828732026-05-27T06:46:51Z
dc.title.none.fl_str_mv Contribution to the study of invariant manifolds and the splitting of separatrices of parabolic points
title Contribution to the study of invariant manifolds and the splitting of separatrices of parabolic points
spellingShingle Contribution to the study of invariant manifolds and the splitting of separatrices of parabolic points
Baldomá, Inmaculada
Varietats diferenciables
Sistemes dinàmics diferenciables
Sistemes hamiltonians
Differentiable manifolds
Differentiable dynamical systems
Hamiltonian systems
title_short Contribution to the study of invariant manifolds and the splitting of separatrices of parabolic points
title_full Contribution to the study of invariant manifolds and the splitting of separatrices of parabolic points
title_fullStr Contribution to the study of invariant manifolds and the splitting of separatrices of parabolic points
title_full_unstemmed Contribution to the study of invariant manifolds and the splitting of separatrices of parabolic points
title_sort Contribution to the study of invariant manifolds and the splitting of separatrices of parabolic points
dc.creator.none.fl_str_mv Baldomá, Inmaculada
author Baldomá, Inmaculada
author_facet Baldomá, Inmaculada
author_role author
dc.contributor.none.fl_str_mv Fontich, Ernest, 1955-
Universitat de Barcelona. Departament de Matemàtica Aplicada i Anàlisi
dc.subject.none.fl_str_mv Varietats diferenciables
Sistemes dinàmics diferenciables
Sistemes hamiltonians
Differentiable manifolds
Differentiable dynamical systems
Hamiltonian systems
topic Varietats diferenciables
Sistemes dinàmics diferenciables
Sistemes hamiltonians
Differentiable manifolds
Differentiable dynamical systems
Hamiltonian systems
description [eng] In general, when beginning to explore any scientific field, one focuses on the generic situations; that is, one centers on the behaviours that appear in “most” of the cases encountered in practice. This methodology allows an easier understanding of the problem, since the non-generic (or degenerate) cases are left out (at least a priori) in a first approach. This way, the casuistic is simpler and the general theory can be developed more easily. Although this is a good scientific procedure, the aim of Science is to explain reality in the most complete way possible. So, when the general case has been already described (perhaps not completely, but at least in a good part), one should study the non-generic cases: the exceptions. It should not be forgotten that, in nature, not all the processes follow a general rule. The exceptional cases often provide new types of behaviour. Therefore, a lot can be learned from the exceptions, as much at an intrinsic level (situations that differ from the general qualitative behaviour) as for the new techniques that are developed in order to understand them. In certain contexts, it is generic to encounter degenerate cases. Let us think, for instance, about the case of parametric families, f(mi), which describe different behaviours depending on the value of mi. In this situation, it is generic (that is, it occurs in most of the families) to find values of the parameter f(mi)(0) for which the behaviour of f(mi)(0) is degenerate.
publishDate 2001
dc.date.none.fl_str_mv 2001
dc.type.none.fl_str_mv info:eu-repo/semantics/doctoralThesis
info:eu-repo/semantics/publishedVersion
format doctoralThesis
status_str publishedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/2445/182873
http://hdl.handle.net/10803/673362
url https://hdl.handle.net/2445/182873
http://hdl.handle.net/10803/673362
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.rights.none.fl_str_mv cc by-nc-sa (c) Baldomá, Inmaculada, 2022
http://creativecommons.org/licenses/by-nc-sa/3.0/es/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv cc by-nc-sa (c) Baldomá, Inmaculada, 2022
http://creativecommons.org/licenses/by-nc-sa/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Universitat de Barcelona
publisher.none.fl_str_mv Universitat de Barcelona
dc.source.none.fl_str_mv Tesis Doctorals - Departament - Matemàtica Aplicada i Anàlisi
reponame:Dipòsit Digital de la UB
instname:Universidad de Barcelona
instname_str Universidad de Barcelona
reponame_str Dipòsit Digital de la UB
collection Dipòsit Digital de la UB
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869407732915765248
score 15,301603

Registos relacionados