Continua as minimal sets of homeomorphisms of S^2

Let $f$ be an orientation preserving homeomorphism of $S^2$ which has a (nontrivial) 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.

No reviews yet.

No comments yet.