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Bifurcations and catastrophes. Geometry of solutions to nonlinear problems. Transl. from the French by David Chillingworth. (English) Zbl 0959.37002

Universitext. Berlin: Springer. viii, 301 p. (2000).
For the French original (Paris, Ellipses 1989) see Zbl 0907.58002. This book is an introduction to the main ideas of the modern global analysis. It is based on the author’s lecture course at the École Polytechnique (Paris).
Contents: 1. Local Inversion. 2. Submanifolds. 3. Transversality Theorems. 4. Classification of Differentiable Functions. 5. Catastrophe Theory. 6. Vector Fields. 7. Linear Vector Fields. 8. Singular Points of Vector Fields. 9. Closed Orbits – Structural Stability. 10. Bifurcations of Phase Portraits.
The style of the book is simultaneously very clear and deep. The book will be useful both for the beginners and for specialists in nonlinear analysis, dynamical systems, and bifurcation theory since it not only describes the language, basic ideas, and main constructions of global analysis but also contains very interesting historical and philosophical comments.

MSC:

37-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to dynamical systems and ergodic theory
58-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to global analysis
37Cxx Smooth dynamical systems: general theory
37Dxx Dynamical systems with hyperbolic behavior
58Cxx Calculus on manifolds; nonlinear operators
58Kxx Theory of singularities and catastrophe theory

Citations:

Zbl 0907.58002
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