Compact global chaotic attractors of discrete control systems. (English) Zbl 1338.37023
Let \(\mathcal{M}\) be a compact subset of the space of all continuous mappings \(f:W\to W\) on a complete metric space \(W\). In the paper under review, the author gives sufficient conditions for the existence of compact global attractors for a family of discrete control systems (cocycles) in the case when \(\mathcal{M}\) is finite (Section 3), and also in the general case when \(\mathcal{M}\) contains an infinite number of mappings which are not necessarily invertible (Section 4). Furthermore, the author gives a complete description of the dynamics of global attractors. The results in this paper extend and improve some existing results in the field.
Reviewer: Nicolae Lupa (Timisoara)
MSC:
| 37B25 | Stability of topological dynamical systems |
| 37B55 | Topological dynamics of nonautonomous systems |
| 93C10 | Nonlinear systems in control theory |
| 93C55 | Discrete-time control/observation systems |
Keywords:
global attractor; set-valued dynamical system; control system; chaotic attractor; collage; cocycleReferences:
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