Fundamentals of dynamical systems and bifurcation theory. (English) Zbl 0777.58027

Medveď, Milan

Bristol, Bratislava: Adam Hilger, Ister Science Press Ltd.. viii, 293 p. (1992).

This monograph is a textbook of graduate school level on fundamentals of dynamical systems. After the introduction (foundations of algebra, topology, mathematical analysis and theory of differential equations) the author explains on foundations of the theory of differentiable manifolds and differential manifolds and differentiable mappings, vector fields and dynamical systems, invariant manifolds, generic bifurcations of vector fields and diffeomorphisms, and contemporary theory of dynamical systems (generic bifurcations of multi-parameter systems of vector fields, global theory of dynamical systems, Šil’nikov bifurcation, global Hopf bifurcation and attractors and chaotic sets).

Reviewer: Y.Kozai (Tokyo)

MSC:

37G99	Local and nonlocal bifurcation theory for dynamical systems
58C25	Differentiable maps on manifolds
58A05	Differentiable manifolds, foundations
58-02	Research exposition (monographs, survey articles) pertaining to global analysis
58A40	Differential spaces

Keywords:

dynamical systems; differentiable manifolds; differential manifolds; bifurcations