---

＜電子ブック＞
Normal Forms and Unfoldings for Local Dynamical Systems / by James Murdock
(Springer Monographs in Mathematics. ISSN:21969922)

版	1st ed. 2003.
出版者	(New York, NY : Springer New York : Imprint: Springer)
出版年	2003
本文言語	英語
大きさ	XX, 500 p : online resource
著者標目	*Murdock, James author SpringerLink (Online service)
件　名	LCSH:Differential equations LCSH:Mathematics LCSH:Mathematical physics FREE:Differential Equations FREE:Applications of Mathematics FREE:Theoretical, Mathematical and Computational Physics
一般注記	Preface -- 1. Two Examples -- 2. The splitting problem for linear operators -- 3. Linear Normal Forms -- 4. Nonlinear Normal Forms -- 5. Geometrical Structures in Normal Forms -- 6. Selected Topics in Local Bifurcation Theory -- Appendix A: Rings -- Appendix B: Modules -- Appendix C: Format 2b: Generated Recursive (Hori) -- Appendix D: Format 2c: Generated Recursive (Deprit) -- Appendix E: On Some Algorithms in Linear Algebra -- Bibliography -- Index 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 HTTP:URL=https://doi.org/10.1007/b97515

 類似資料