Bifurcations, robustness and shape of attractors of discrete dynamical systems. (English) Zbl 1434.37015
The aim of this paper is to study the global properties of the topological nature of the attractors of discrete dynamical systems and the stability or change of these properties when the system is disturbed or bifurcated. The authors study the Andronov-Hopf bifurcation for homeomorphisms of the plane and robustness properties for attractors of such homeomorphisms. The relationships between flow attractors and attractors of homeomorphisms in \(\mathbb{R}^n\) are investigated, as well as the Čech homology and the shape of fractals in the plane. Some remarks about the recent theory of Conley attractors for IFS are discussed.
Reviewer: Irina V. Konopleva (Ul’yanovsk)
MSC:
| 37C70 | Attractors and repellers of smooth dynamical systems and their topological structure |
| 37E30 | Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces |
| 37G35 | Dynamical aspects of attractors and their bifurcations |
| 37C20 | Generic properties, structural stability of dynamical systems |
| 37B25 | Stability of topological dynamical systems |
| 28A80 | Fractals |
| 55N05 | Čech types |
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