Continua as minimal sets of homeomorphisms of S^2

Details Continua as minimal sets of homeomorphisms of S^2 Continua as minimal sets of homeomorphisms of S^2

2010-05-03

arxiv.org/abs/1005.0360v2

Mathematics

Dynamical Systems

16 pages, 15 figures

Scientific paper

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.

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