
Differential Geometry Applied To Dynamical Systems (With Cd-rom)
(With CD-ROM)
Jean-Marc Ginoux(Author)
World Scientific Publishing Co Pte Ltd
Will be published approx. on 6. April 2009
Book
Paperback/Softback
340 pages
978-981-4277-14-3 (ISBN)
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.
More details
Series
Language
English
Place of publication
Singapore
Singapore
Target group
College/higher education
Professional and scholarly
Graduate students, researchers and academics in nonlinear dynamics.
Dimensions
Height: 234 mm
Width: 157 mm
Thickness: 20 mm
Weight
680 gr
ISBN-13
978-981-4277-14-3 (9789814277143)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Person
Content
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.