Differential Geometry Applied To Dynamical Systems With Cd rom is popular PDF and ePub book, written by Jean-marc Ginoux in 2009-04-03, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Differential Geometry Applied To Dynamical Systems With Cd rom can be Read Online from any device for your convenience.
Differential Geometry Applied To Dynamical Systems With Cd rom Book PDF 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 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.
Detail Book of Differential Geometry Applied To Dynamical Systems With Cd rom PDF
- Author : Jean-marc Ginoux
- Release : 03 April 2009
- Publisher : World Scientific
- ISBN : 9789814467636
- Genre : Mathematics
- Total Page : 341 pages
- Language : English
- PDF File Size : 18,5 Mb
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