Normal Forms and Unfoldings for Local Dynamical Systems

• Main Author: Murdock, James (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York : Imprint: Springer, 2003.
• Series: Springer Monographs in Mathematics,
• Subjects: Mathematics.; Differential equations.; Applied mathematics.; Engineering mathematics.; Physics.; Ordinary Differential Equations.; Applications of Mathematics.; Theoretical, Mathematical and Computational Physics.

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...

Table of Contents:

• 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.