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The Conley index and non-existence of minimal homeomorphisms. (English) Zbl 0948.37005
The paper is devoted to the following question: Does there exist a homeomorphism of \(\mathbb{R}^n\) or \(\mathbb{R}^n\setminus \{pt\}\) in which every complete orbit is dense? Such a homeomorphism is called minimal because the smallest nonempty closed invariant subset is the entire space. The author gives an alternative proof of the theorem of P. L. Calvez and J.-C. Yoccoz on the non-existence of minimal homeomorphism of the finitely punctured plane which is based on the use of the Conley index.

37B30 Index theory for dynamical systems, Morse-Conley indices
37D10 Invariant manifold theory for dynamical systems