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 \({\mathbb {R}}^{n}\). 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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Acknowledgements
The authors are grateful to Jerzy Dydak for inspiring conversations. They also would like to express their gratitude to the referee for his useful suggestions that have helped to improve the quality of the manuscript.
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The authors are partially supported by the Spanish Ministerio de Ciencia, Innovación y Universidades (Grant PGC2018-098321-B-I00).
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Barge, H., Giraldo, A. & Sanjurjo, J.M.R. Bifurcations, robustness and shape of attractors of discrete dynamical systems. J. Fixed Point Theory Appl. 22, 29 (2020). https://doi.org/10.1007/s11784-020-0770-3
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DOI: https://doi.org/10.1007/s11784-020-0770-3