Can I read $R$-closed homeomorphisms on surfaces on EtoBox?

$R$-closed homeomorphisms on surfaces by Yokoyama, Tomoo is a scholarly article available to read on EtoBox.

What is $R$-closed homeomorphisms on surfaces about?

Let $f$ be an $R$-closed homeomorphism on a connected orientable closed surface $M$. In this paper, we show that If $M$ has genus more than one, then each minimal set is either a periodic orbit or an extension of a Cantor set. If $M = \mathbb{T}^2$ and $f$ is neither minimal nor periodic, then either each minimal set is finite disjoint union of essential circloids or there is a minimal set which is an extension of a Cantor set. If $M = \mathbb{S}^2$ and $f$ is not periodic but orientation-preserving (resp. reversing), then the minimal sets of $f$ (resp. $f^2$) are exactly two fixed points and other circloids and $\mathbb{S}^2/\widetilde{f} \cong [0, 1]$.

Author

Yokoyama, Tomoo

Published

2012

Language

EN