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arXiv · 1802.05454

Bifurcations, robustness and shape theory of attractors of discrete dynamical systems

Héctor Barge·Antonio Giraldo·José M. R. Sanjurjo
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Abstract

We study in this paper global properties, mainly of topological nature, of attractors of discrete dynamical systems. We consider the Andronov-Hopf bifurcation for homeomorphisms of the plane and establish some robustness properties for attractors of such homeomorphisms. We also give relations between attractors of flows and quasi-attractors of homeomorphisms in Rn. Finally, we give a result on the shape (in the sense of Borsuk) of invariant sets of IFSs on the plane, and make some remarks about the recent theory of Conley attractors for IFS.

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Héctor Barge, Antonio Giraldo, José M. R. Sanjurjo. 2018-02-15. Bifurcations, robustness and shape theory of attractors of discrete dynamical systems. https://doi.org/10.1007/s11784-020-0770-3

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