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  1. Bog
  2. Geometri
  3. Differential- og Riemannsk geometri

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

Af: Jean-marc Ginoux Engelsk Hardback

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

Af: Jean-marc Ginoux Engelsk Hardback
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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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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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Se mere i:
Produktdetaljer
Sprog: Engelsk
Sider: 340
ISBN-13: 9789814277143
Indbinding: Hardback
Udgave:
ISBN-10: 9814277142
Kategori: Differential- og Riemannsk geometri
Udg. Dato: 6 apr 2009
Længde: 21mm
Bredde: 162mm
Højde: 237mm
Forlag: World Scientific Publishing Co Pte Ltd
Oplagsdato: 6 apr 2009
Forfatter(e): Jean-marc Ginoux
Forfatter(e) Jean-marc Ginoux

Kategori Differential- og Riemannsk geometri

ISBN-13 9789814277143

Sprog Engelsk

Indbinding Hardback

Sider 340

Udgave

Længde 21mm

Bredde 162mm

Højde 237mm

Udg. Dato 6 apr 2009

Oplagsdato 6 apr 2009

Forlag World Scientific Publishing Co Pte Ltd

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