Based on a lecture course at the Ecole Polytechnique (Paris), this text gives a rigorous introduction to many of the key ideas in nonlinear analysis, dynamical systems and bifurcation theory including catastrophe theory. Wherever appropriate it emphasizes a geometrical or coordinate-free approach which allows a clear focus on the essential mathematical structures. Taking a unified view, it brings out features common to different branches of the subject while giving ample references for more advanced or technical developments.
Author(s): Michel Demazure (auth.)
Series: Universitext
Edition: 1
Publisher: Springer-Verlag Berlin Heidelberg
Year: 2000
Language: English
Pages: 304
Tags: Differential Geometry; Global Analysis and Analysis on Manifolds; Dynamical Systems and Ergodic Theory
Front Matter....Pages I-VIII
Introduction....Pages 1-11
Local Inversion....Pages 13-30
Submanifolds....Pages 31-61
Transversality Theorems....Pages 63-86
Classification of Differentiable Functions....Pages 87-113
Catastrophe Theory....Pages 115-145
Vector Fields....Pages 147-177
Linear Vector Fields....Pages 179-217
Singular Points of Vector Fields....Pages 219-247
Closed Orbits — Structural Stability....Pages 249-268
Bifurcations of Phase Portraits....Pages 269-292
Back Matter....Pages 293-303
