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Differential geometry applied to dyn...

Ginoux, Jean-Marc.

Differential geometry applied to dynamical systems

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Differential geometry applied to dynamical systemsJean-Marc Ginoux.
作者:	Ginoux, Jean-Marc.
出版者:	Singapore ;World Scientific,c2009.
面頁冊數:	xxvii, 312 p. :ill. (some col.)
標題:	Dynamics.
電子資源:	http://www.worldscientific.com/worldscibooks/10.1142/7333#t=toc
ISBN:	9789814277150 (electronic bk.)

Differential geometry applied to dynamical systems
Ginoux, Jean-Marc.

Differential geometry applied to dynamical systems[electronic resouce] /Jean-Marc Ginoux. - Singapore ;World Scientific,c2009. - xxvii, 312 p. :ill. (some col.) - World scientific series on nonlinear science. Series A. ;v. 66. - World Scientific series on nonlinear science.Series A,Monographs and treatises ;v. 45..

Includes bibliographical references (p. 297-307) and index.

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.

Electronic reproduction.
Singapore :
World Scientific Publishing Co.,
2009.

System requirements: Adobe Acrobat Reader.

ISBN: 9789814277150 (electronic bk.)Subjects--Topical Terms:

189568
Dynamics.

LC Class. No.: QA845

Dewey Class. No.: 531.11

Differential geometry applied to dynamical systems
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490 1 $a World scientific series on nonlinear science. Series A. ; $v v. 66
504 $a Includes bibliographical references (p. 297-307) and index.
520 $a 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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