Continua as minimal sets of homeomorphisms of S^2

Shigenori Matsumoto; Hiromichi Nakayama

Continua as minimal sets of homeomorphisms of S^2

Dynamical Systems 2013-06-06 v2

Authors: Shigenori Matsumoto , Hiromichi Nakayama

Abstract

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 Carath\'eodory rotation number of an invariant component is irrational.

Keywords

homeomorphisms of S^2 minimal sets continua rotation number wandering domains orientation preserving

Cite

@article{arxiv.1005.0360,
  title  = {Continua as minimal sets of homeomorphisms of S^2},
  author = {Shigenori Matsumoto and Hiromichi Nakayama},
  journal= {arXiv preprint arXiv:1005.0360},
  year   = {2013}
}

Comments

16 pages, 15 figures

Related papers

View all related →