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Chaotic dynamics in two-dimensional noninvertible maps. (English) Zbl 0906.58027

World Scientific Series on Nonlinear Science. Series A. 20. Singapore: World Scientific. xxii, 602 p. (1996).
From the Preface: “The monograph does not pretend to be a mathematical treatise on discrete dynamical systems. Its purpose is far more modest and consists in:
(a) giving the properties of the “critical set” basic tool, and its different uses for solving problems of the qualitative theory of discrete dynamical systems;
(b) understanding dominating internal mechanisms of models in the form of noninvertible maps, and preserving a phenomenological transparency through the simplest possible examples, from which perhaps “standard” mathematical theories might be elaborated;
(c) stimulating some ways of research, and facilitating the study of practical problems in engineering, physics, etc.”
Contents: Chapter 1. Generalities on dynamical systems and maps. Chapter 2. One-dimensional noninvertible maps. Chapter 3. Two-dimensional noninvertible maps. Properties of critical curves. Chapter 4. Absorbing areas and chaotic areas of two-dimensional noninvertible maps. Chapter 5. Basins and their bifurcations. Chapter 6. On some properties of invariant sets of two-dimensional noninvertible maps.

MSC:

37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37-02 Research exposition (monographs, survey articles) pertaining to dynamical systems and ergodic theory
34-02 Research exposition (monographs, survey articles) pertaining to ordinary differential equations
37G99 Local and nonlocal bifurcation theory for dynamical systems
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