Differential Geometry Applied to Dynamical Systems PDF
By:Jean-Marc Ginoux
Published on 2009 by World Scientific
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 OCo or the flow OCo 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.
This Book was ranked at 20 by Google Books for keyword Applied.
Book ID of Differential Geometry Applied to Dynamical Systems's Books is t2xkDQAAQBAJ, Book which was written byJean-Marc Ginouxhave ETAG "KfpY3tfFcks"
Book which was published by World Scientific since 2009 have ISBNs, ISBN 13 Code is 9789814277150 and ISBN 10 Code is 9814277150
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Book which have "340 Pages" is Printed at BOOK under CategoryScience
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Download Differential Geometry Applied to Dynamical Systems PDF
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