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.

中文翻译：

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离散动力系统的分叉，鲁棒性和吸引子的形状

我们在本文中研究离散动力系统吸引子的整体性质，主要是拓扑性质。我们考虑平面的同胚性的Andronov-Hopf分叉，并为此类同胚性的吸引子建立了一些鲁棒性。我们还给出了\（{\ mathbb {R}} ^ {n} \）中的流吸引子与同胚的拟吸引子之间的关系。最后，我们给出了平面上IFS不变集的形状（就Borsuk而言），并对最近关于IFS的Conley吸引子理论作了一些评论。