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Differential geometry applied to dynamical systems

Author: Jean-Marc Ginoux
Publisher: Hackensack, N.J. : World Scientific, 2009.
Series: World Scientific series on nonlinear science., Series A,, Monographs and treatises ;, vol. 66.; World Scientific series on nonlinear science., Series A,, Monographs and treatises ;, v. 66.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Database:WorldCat
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Ginoux, Jean-Marc.
Differential geometry applied to dynamical systems.
Hackensack, N.J. : World Scientific, 2009
(OCoLC)311763235
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Jean-Marc Ginoux
ISBN: 9789814277150 9814277150
OCLC Number: 593212992
Description: 1 online resource (xxvii, 312 pages) : illustrations.
Contents: Differential Equations; Hartman-Grobman Theorem; Liapounoff Stability Theorem; Phase Portraits; Poincare-Bendixson Theorem; Attractors; Strange Attractors; Hamiltonian and Integrable Systems; K A M Theorem; Invariant Sets; Global/Local Invariance; Center Manifold Theorem; Normal Form Theorem; Local Bifurcations of Codimension 1; Hopf Bifurcation, Slow-Fast Dynamical Systems; Geometric Singular Perturbation Theory; Darboux Theory of Integrability; Differential Geometry; Generalized Frenet Moving Frame; Curvatures of Trajectory Curves; Flow Curvature Manifold; Flow Curvature Method; Van der Pol Model; FitzHugh-Nagumo Model; Pikovskii-Rabinovich-Trakhtengerts Model; Rikitake Model; Chua's Model; Lorenz Model.
Series Title: World Scientific series on nonlinear science., Series A,, Monographs and treatises ;, vol. 66.; World Scientific series on nonlinear science., Series A,, Monographs and treatises ;, v. 66.
Responsibility: Jean-Marc Ginoux.

Abstract:

Presents a fresh approach called Flow Curvature Method that applies Differential Geometry to Dynamical Systems.  Read more...

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