James Murdock Normal Forms and Unfoldings for Local Dynamical Systems 9781441930132

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Автор: James Murdock
Название: Normal Forms and Unfoldings for Local Dynamical Systems
ISBN: 9781441930132
Издательство: Springer
Классификация:

Основы высшей математики и математический анализ

Прикладная математика

Математика для учёных

Математика для инженеров

ISBN-10: 1441930132
Обложка/Формат: Paperback
Страницы: 500
Вес: 0.72 кг.
Дата издания: 01.12.2010
Серия: Springer Monographs in Mathematics
Язык: English
Размер: 234 x 156 x 26
Основная тема: Mathematics
Ссылка на Издательство: Link
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Поставляется из: Германии
Описание: The subject of local dynamical systems is concerned with the following two questions: 1. Given an nn 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.

Normal Forms and Unfoldings for Local Dynamical Systems, James Murdock