English

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

Dynamical Systems 2020-03-18 v1

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.

Keywords

Cite

@article{arxiv.1802.05454,
  title  = {Bifurcations, robustness and shape theory of attractors of discrete dynamical systems},
  author = {Héctor Barge and Antonio Giraldo and José M. R. Sanjurjo},
  journal= {arXiv preprint arXiv:1802.05454},
  year   = {2020}
}

Comments

14 pages, 2 figures, Comments are welcomed