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arXiv · 1410.5857

Density of the set of symbolic dynamics with all ergodic measures supported on periodic orbits

T. C. Batista·J. S. Gonschorowski·F. A. Tal
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Abstract

Let $K$ be the Cantor set. We prove that arbitrarily close to a homeomorphism $T:K\rightarrow K$ there exists a homeomorphism $\widetilde T:K\rightarrow K$ such that the $α$-limit and the $ω$-limit of every orbit is a periodic orbit. We also prove that arbitrarily close to an endomorphism $T:K\rightarrow K$ there exists an endomorphism $\widetilde T:K\rightarrow K$ close to $T$ such that every orbit is finally periodic.

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T. C. Batista, J. S. Gonschorowski, F. A. Tal. 2015-02-03. Density of the set of symbolic dynamics with all ergodic measures supported on periodic orbits. https://arxiv.org/abs/1410.5857

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