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

dc.contributor
Universitat de Barcelona. Departament de Matemàtica Aplicada i Anàlisi
dc.contributor.author
Baldomá, Inmaculada
dc.date.accessioned
2022-02-01T11:56:43Z
dc.date.available
2022-02-01T11:56:43Z
dc.date.issued
2001-01-01
dc.identifier.uri
http://hdl.handle.net/10803/673362
dc.description.abstract
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.
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dc.format.extent
319 p.
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dc.format.mimetype
application/pdf
dc.language.iso
eng
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dc.publisher
Universitat de Barcelona
dc.rights.license
L'accés als continguts d'aquesta tesi queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commons: http://creativecommons.org/licenses/by-nc-sa/4.0/
dc.source
TDX (Tesis Doctorals en Xarxa)
dc.subject
Varietats diferenciables
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dc.subject
Variedades diferenciables
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dc.subject
Differentiable manifolds
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dc.subject
Sistemes dinàmics diferenciables
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dc.subject
Sistemas dinámicos diferenciales
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dc.subject
Differentiable dynamical systems
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dc.subject
Sistemes hamiltonians
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dc.subject
Sistemas de Hamilton
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dc.subject
Hamiltonian systems
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dc.subject.other
Ciències Experimentals i Matemàtiques
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dc.title
Contribution to the study of invariant manifolds and the splitting of separatrices of parabolic points
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dc.type
info:eu-repo/semantics/doctoralThesis
dc.type
info:eu-repo/semantics/publishedVersion
dc.subject.udc
51
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dc.contributor.authoremail
immaculada_baldoma@upc.edu
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dc.contributor.authoremailshow
false
en_US
dc.contributor.director
Fontich, Ernest, 1955-
dc.embargo.terms
cap
en_US
dc.rights.accessLevel
info:eu-repo/semantics/openAccess


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