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The Parametrisation method for invariant manifolds of tori in Skew-product lattices and an entire transcendental family with a persistent Siegel disk

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Title: The Parametrisation method for invariant manifolds of tori in Skew-product lattices and an entire transcendental family with a persistent Siegel disk
Authors: Berenguel Montoro, Rubén
Contributors: University/Department: Universitat de Barcelona. Departament de Matemàtica Aplicada i Anàlisi
Thesis Advisors: Fagella Rabionet, Núria, Fontich, Ernest, 1955-
Source: TDX (Tesis Doctorals en Xarxa)
Publisher Information: Universitat de Barcelona, 2016.
Publication Year: 2016
Physical Description: 236 p.
Subject Terms: Sistemes dinàmics diferenciables, Sistemas dinámicos diferenciales, Differentiable dynamical systems, Invariants, Invariantes, Teoria dels reticles, Teoría reticular, Lattice theory, Tor (Geometria), Tor (Geometría), Torus (Geometry), Pertorbació (Matemàtica), Perturbación (Matemáticas), Perturbation (Mathematics), Varietats (Matemàtica), Variedades (Matemáticas), Manifolds (Mathematics), Funcions holomorfes, Funciones holomorfas, Holomorphic functions, Ciències Experimentals i Matemàtiques
Description: In this thesis we consider two different problems in the theory of dynamical systems. Dynamical systems cover a wide array of subjects, from finite dimensional to infinite dimensional, from analytic to statistical viewpoints and through all gradations in-between. No matter the aspect or tool considered, the study of any dynamical system is concerned in some way or another with the evolution of points through the action of a map. The simplest question to ask of a dynamical system is then which points are invariant? Once we have an answer to this question we can proceed to study the dynamics in a neighborhood of them. In general we find invariant subsets containing the fixed point which provide very relevant information.
Description (Translated): En aquest treball considerem dos problemes en la teoria dels sistemes dinàmics. El camp dels sistemes dinàmics abarca un ampli espectre de temes, des de sistemes finit dimensionals a infinit dimensionals, des de punts de vista analítics a estadístics, amb totes les possibles gradacions intermitges. Obviant l’aspecte o eina considerats, l’estudi de qualsevol sistema dinàmic es centra, d’una manera o una altra, en l’estudi de l’evolució de punts sota l’acció d’una aplicación. La pregunta més simple que podem fer-li a un sistema dinàmic és: ¿llavors quins punts són invariants? Un cop en tenim una resposta podem passar a estudiar la dinàmica en un entorn d’ells. En general, hi trobem conjunts invariants que contenen els punts fixos, i que ens proveeixen d’informació molt rellevant.
Document Type: Dissertation/Thesis
File Description: application/pdf
Language: English
Access URL: http://hdl.handle.net/10803/396126
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/4.0/
Accession Number: edstdx.10803.396126
Database: TDX
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  – Url: http://hdl.handle.net/10803/396126#
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PubType: Dissertation/ Thesis
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  Data: The Parametrisation method for invariant manifolds of tori in Skew-product lattices and an entire transcendental family with a persistent Siegel disk
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  Data: <searchLink fieldCode="AR" term="%22Berenguel+Montoro%2C+Rubén%22">Berenguel Montoro, Rubén</searchLink>
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  Label: Contributors
  Group: Au
  Data: University/Department: Universitat de Barcelona. Departament de Matemàtica Aplicada i Anàlisi
– Name: Author
  Label: Thesis Advisors
  Group: Au
  Data: Fagella Rabionet, Núria<br />Fontich, Ernest, 1955-
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  Data: TDX (Tesis Doctorals en Xarxa)
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  Data: Universitat de Barcelona, 2016.
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  Data: 2016
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  Data: 236 p.
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  Group: Ab
  Data: In this thesis we consider two different problems in the theory of dynamical systems. Dynamical systems cover a wide array of subjects, from finite dimensional to infinite dimensional, from analytic to statistical viewpoints and through all gradations in-between. No matter the aspect or tool considered, the study of any dynamical system is concerned in some way or another with the evolution of points through the action of a map. The simplest question to ask of a dynamical system is then which points are invariant? Once we have an answer to this question we can proceed to study the dynamics in a neighborhood of them. In general we find invariant subsets containing the fixed point which provide very relevant information.
– Name: Abstract
  Label: Description (Translated)
  Group: Ab
  Data: En aquest treball considerem dos problemes en la teoria dels sistemes dinàmics. El camp dels sistemes dinàmics abarca un ampli espectre de temes, des de sistemes finit dimensionals a infinit dimensionals, des de punts de vista analítics a estadístics, amb totes les possibles gradacions intermitges. Obviant l’aspecte o eina considerats, l’estudi de qualsevol sistema dinàmic es centra, d’una manera o una altra, en l’estudi de l’evolució de punts sota l’acció d’una aplicación. La pregunta més simple que podem fer-li a un sistema dinàmic és: ¿llavors quins punts són invariants? Un cop en tenim una resposta podem passar a estudiar la dinàmica en un entorn d’ells. En general, hi trobem conjunts invariants que contenen els punts fixos, i que ens proveeixen d’informació molt rellevant.
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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/4.0/
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RecordInfo BibRecord:
  BibEntity:
    Languages:
      – Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 236
    Subjects:
      – SubjectFull: Sistemes dinàmics diferenciables
        Type: general
      – SubjectFull: Sistemas dinámicos diferenciales
        Type: general
      – SubjectFull: Differentiable dynamical systems
        Type: general
      – SubjectFull: Invariants
        Type: general
      – SubjectFull: Invariantes
        Type: general
      – SubjectFull: Teoria dels reticles
        Type: general
      – SubjectFull: Teoría reticular
        Type: general
      – SubjectFull: Lattice theory
        Type: general
      – SubjectFull: Tor (Geometria)
        Type: general
      – SubjectFull: Tor (Geometría)
        Type: general
      – SubjectFull: Torus (Geometry)
        Type: general
      – SubjectFull: Pertorbació (Matemàtica)
        Type: general
      – SubjectFull: Perturbación (Matemáticas)
        Type: general
      – SubjectFull: Perturbation (Mathematics)
        Type: general
      – SubjectFull: Varietats (Matemàtica)
        Type: general
      – SubjectFull: Variedades (Matemáticas)
        Type: general
      – SubjectFull: Manifolds (Mathematics)
        Type: general
      – SubjectFull: Funcions holomorfes
        Type: general
      – SubjectFull: Funciones holomorfas
        Type: general
      – SubjectFull: Holomorphic functions
        Type: general
      – SubjectFull: Ciències Experimentals i Matemàtiques
        Type: general
    Titles:
      – TitleFull: The Parametrisation method for invariant manifolds of tori in Skew-product lattices and an entire transcendental family with a persistent Siegel disk
        Type: main
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          Name:
            NameFull: Berenguel Montoro, Rubén
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          Dates:
            – D: 02
              M: 02
              Type: published
              Y: 2016
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