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Differential Geometry Applied To Dynamical Systems: (With Cd-rom)

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Title: Differential Geometry Applied To Dynamical Systems: (With Cd-rom)
Description: This book aims to present a new approach called Flow Curvature Method that applies Differential Geometry to Dynamical Systems. Hence, for a trajectory curve, an integral of any n-dimensional dynamical system as a curve in Euclidean n-space, the curvature of the trajectory — or the flow — may be analytically computed. Then, the location of the points where the curvature of the flow vanishes defines a manifold called flow curvature manifold. Such a manifold being defined from the time derivatives of the velocity vector field, contains information about the dynamics of the system, hence identifying the main features of the system such as fixed points and their stability, local bifurcations of codimension one, center manifold equation, normal forms, linear invariant manifolds (straight lines, planes, hyperplanes).In the case of singularly perturbed systems or slow-fast dynamical systems, the flow curvature manifold directly provides the slow invariant manifold analytical equation associated with such systems. Also, starting from the flow curvature manifold, it will be demonstrated how to find again the corresponding dynamical system, thus solving the inverse problem.
Authors: Jean-marc Ginoux
Resource Type: eBook.
Subjects: Geometry, Differential, Dynamics
Categories: MATHEMATICS / Geometry / Differential, MATHEMATICS / Algebra / Linear, MATHEMATICS / Applied
Database: eBook Collection (EBSCOhost)
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  – Type: ebook-pdf
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  Availability: 0
Header DbId: nlebk
DbLabel: eBook Collection (EBSCOhost)
An: 305321
RelevancyScore: 1025
AccessLevel: 6
PubType: eBook
PubTypeId: ebook
PreciseRelevancyScore: 1024.62744140625
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  Label: Title
  Group: Ti
  Data: Differential Geometry Applied To Dynamical Systems: (With Cd-rom)
– Name: Abstract
  Label: Description
  Group: Ab
  Data: This book aims to present a new approach called Flow Curvature Method that applies Differential Geometry to Dynamical Systems. Hence, for a trajectory curve, an integral of any n-dimensional dynamical system as a curve in Euclidean n-space, the curvature of the trajectory — or the flow — may be analytically computed. Then, the location of the points where the curvature of the flow vanishes defines a manifold called flow curvature manifold. Such a manifold being defined from the time derivatives of the velocity vector field, contains information about the dynamics of the system, hence identifying the main features of the system such as fixed points and their stability, local bifurcations of codimension one, center manifold equation, normal forms, linear invariant manifolds (straight lines, planes, hyperplanes).In the case of singularly perturbed systems or slow-fast dynamical systems, the flow curvature manifold directly provides the slow invariant manifold analytical equation associated with such systems. Also, starting from the flow curvature manifold, it will be demonstrated how to find again the corresponding dynamical system, thus solving the inverse problem.
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  Data: eBook.
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  Data: <searchLink fieldCode="DE" term="%22Geometry%2C+Differential%22">Geometry, Differential</searchLink><br /><searchLink fieldCode="DE" term="%22Dynamics%22">Dynamics</searchLink>
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RecordInfo BibRecord:
  BibEntity:
    Classifications:
      – Code: 531.11
        Scheme: ddc
        Type: prePub
    Languages:
      – Code: eng
        Text: English
    Subjects:
      – SubjectFull: Geometry, Differential
        Type: general
      – SubjectFull: Dynamics
        Type: general
    Titles:
      – TitleFull: Differential Geometry Applied To Dynamical Systems: (With Cd-rom)
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Jean-marc Ginoux
      – PersonEntity:
          Name:
            NameFull: Jean-marc Ginoux
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 01
              Type: published
              Y: 2009
            – D: 04
              M: 02
              Type: profile
              Y: 2014
          Identifiers:
            – Type: isbn-print
              Value: 9789814277143
            – Type: isbn-electronic
              Value: 9789814277150
          Numbering:
            – Type: volume
              Value: 00066
          Titles:
            – TitleFull: Differential Geometry Applied To Dynamical Systems: (With Cd-rom)
              Type: main
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