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We study in this paper global properties, mainly of topological nature, ofattractors of discrete dynamical systems. We consider the Andronov-Hopfbifurcation for homeomorphisms of the plane and establish some robustnessproperties for attractors of such homeomorphisms. We also give relationsbetween attractors of flows and quasi-attractors of homeomorphisms in Rn.Finally, we give a result on the shape (in the sense of Borsuk) of invariantsets of IFSs on the plane, and make some remarks about the recent theory ofConley attractors for IFS.

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