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

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Title: Contribution to the study of invariant manifolds and the splitting of separatrices of parabolic points
Authors: Baldomá, Inmaculada
Contributors: University/Department: Universitat de Barcelona. Departament de Matemàtica Aplicada i Anàlisi
Thesis Advisors: Fontich, Ernest, 1955-
Source: TDX (Tesis Doctorals en Xarxa)
Publisher Information: Universitat de Barcelona, 2001.
Publication Year: 2001
Physical Description: 319 p.
Subject Terms: Varietats diferenciables, Variedades diferenciables, Differentiable manifolds, Sistemes dinàmics diferenciables, Sistemas dinámicos diferenciales, Differentiable dynamical systems, Sistemes hamiltonians, Sistemas de Hamilton, Hamiltonian systems, Ciències Experimentals i Matemàtiques
Description: 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.
Document Type: Dissertation/Thesis
File Description: application/pdf
Language: English
Access URL: http://hdl.handle.net/10803/673362
Rights: 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/
Accession Number: edstdx.10803.673362
Database: TDX
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  – Url: http://hdl.handle.net/10803/673362#
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PubType: Dissertation/ Thesis
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Items – Name: Title
  Label: Title
  Group: Ti
  Data: Contribution to the study of invariant manifolds and the splitting of separatrices of parabolic points
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Baldomá%2C+Inmaculada%22">Baldomá, Inmaculada</searchLink>
– Name: Author
  Label: Contributors
  Group: Au
  Data: University/Department: Universitat de Barcelona. Departament de Matemàtica Aplicada i Anàlisi
– Name: Author
  Label: Thesis Advisors
  Group: Au
  Data: Fontich, Ernest, 1955-
– Name: TitleSource
  Label: Source
  Group: Src
  Data: TDX (Tesis Doctorals en Xarxa)
– Name: Publisher
  Label: Publisher Information
  Group: PubInfo
  Data: Universitat de Barcelona, 2001.
– Name: DatePubCY
  Label: Publication Year
  Group: Date
  Data: 2001
– Name: PhysDesc
  Label: Physical Description
  Group: PhysDesc
  Data: 319 p.
– Name: Subject
  Label: Subject Terms
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Varietats+diferenciables%22">Varietats diferenciables</searchLink><br /><searchLink fieldCode="DE" term="%22Variedades+diferenciables%22">Variedades diferenciables</searchLink><br /><searchLink fieldCode="DE" term="%22Differentiable+manifolds%22">Differentiable manifolds</searchLink><br /><searchLink fieldCode="DE" term="%22Sistemes+dinàmics+diferenciables%22">Sistemes dinàmics diferenciables</searchLink><br /><searchLink fieldCode="DE" term="%22Sistemas+dinámicos+diferenciales%22">Sistemas dinámicos diferenciales</searchLink><br /><searchLink fieldCode="DE" term="%22Differentiable+dynamical+systems%22">Differentiable dynamical systems</searchLink><br /><searchLink fieldCode="DE" term="%22Sistemes+hamiltonians%22">Sistemes hamiltonians</searchLink><br /><searchLink fieldCode="DE" term="%22Sistemas+de+Hamilton%22">Sistemas de Hamilton</searchLink><br /><searchLink fieldCode="DE" term="%22Hamiltonian+systems%22">Hamiltonian systems</searchLink><br /><searchLink fieldCode="DE" term="%22Ciències+Experimentals+i+Matemàtiques%22">Ciències Experimentals i Matemàtiques</searchLink>
– Name: Abstract
  Label: Description
  Group: Ab
  Data: 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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– Name: Language
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  Data: <link linkTarget="URL" linkTerm="http://hdl.handle.net/10803/673362" linkWindow="_blank">http://hdl.handle.net/10803/673362</link>
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  Data: 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/
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  Label: Accession Number
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  Data: edstdx.10803.673362
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RecordInfo BibRecord:
  BibEntity:
    Languages:
      – Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 319
    Subjects:
      – SubjectFull: Varietats diferenciables
        Type: general
      – SubjectFull: Variedades diferenciables
        Type: general
      – SubjectFull: Differentiable manifolds
        Type: general
      – SubjectFull: Sistemes dinàmics diferenciables
        Type: general
      – SubjectFull: Sistemas dinámicos diferenciales
        Type: general
      – SubjectFull: Differentiable dynamical systems
        Type: general
      – SubjectFull: Sistemes hamiltonians
        Type: general
      – SubjectFull: Sistemas de Hamilton
        Type: general
      – SubjectFull: Hamiltonian systems
        Type: general
      – SubjectFull: Ciències Experimentals i Matemàtiques
        Type: general
    Titles:
      – TitleFull: Contribution to the study of invariant manifolds and the splitting of separatrices of parabolic points
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Baldomá, Inmaculada
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          Dates:
            – D: 01
              M: 01
              Type: published
              Y: 2001
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