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arXiv · 1208.1536

Toral or non locally connected minimal sets for suspensions of $R$-closed surface homeomorphisms

Tomoo Yokoyama
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Abstract

Let $M$ be an orientable connected closed surface and $f$ be an $R$-closed homeomorphism on $M$ which is isotopic to identity. Then the suspension of $f$ satisfies one of the following condition: 1) the closure of each element of it is minimal and toral. 2) there is a minimal set which is not locally connected. Moreover, we show that any positive iteration of an $R$-closed homeomorphism on a compact metrizable space is $R$-closed.

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Tomoo Yokoyama. 2012-08-07. Toral or non locally connected minimal sets for suspensions of $R$-closed surface homeomorphisms. https://arxiv.org/abs/1208.1536

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