# Continua as minimal sets of homeomorphisms of $S^2$

### Shigenori Matsumoto

Nihon University of Science and Technology, Tokyo, Japan### Hiromichi Nakayama

Aoyama Gakuin University, Kanagawa, Japan

## Abstract

Let $f$ be an orientation preserving homeomorphism of $S^2$ which has a continuum $X$ as a minimal set. Then there are exactly two connected components of $S^2\setminus X$ which are left invariant by $f$ and all the others are wandering. The Carathéodory rotation number of an invariant component is irrational.

## Cite this article

Shigenori Matsumoto, Hiromichi Nakayama, Continua as minimal sets of homeomorphisms of $S^2$. Enseign. Math. 57 (2011), no. 3, pp. 373–392

DOI 10.4171/LEM/57-3-5