Normal Forms and Unfoldings for Local Dynamical Systems

By:

James Murdock

Format:

Paperback / softback

Series:

Springer Monographs in Mathematics

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Description

The subject of local dynamical systems is concerned with the following two questions: 1. Given an n×n matrix A, describe the behavior, in a neighborhood of the origin, of the solutions of all systems of di?erential equations having a rest point at the origin with linear part Ax, that is, all systems of the form x ? = Ax+··· , n where x? R and the dots denote terms of quadratic and higher order. 2. Describethebehavior(neartheorigin)ofallsystemsclosetoasystem of the type just described. To answer these questions, the following steps are employed: 1. A normal form is obtained for the general system with linear part Ax. The normal form is intended to be the simplest form into which any system of the intended type can be transformed by changing the coordinates in a prescribed manner. 2. An unfolding of the normal form is obtained. This is intended to be the simplest form into which all systems close to the original s- tem can be transformed. It will contain parameters, called unfolding parameters, that are not present in the normal form found in step 1. vi Preface 3. The normal form, or its unfolding, is truncated at some degree k, and the behavior of the truncated system is studied.

Release date Australia

December 1st, 2010

Author

James Murdock

Audience

Professional & Vocational

Edition

Softcover reprint of the original 1st ed. 2003

Illustrations

XX, 500 p.

Pages

500

Series

Springer Monographs in Mathematics

Dimensions

156x234x26

ISBN-13

9781441930132

Product ID

8937953

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