Article contents
Proper minimal sets on compact connected 2-manifolds are nowhere dense
Published online by Cambridge University Press: 01 June 2008
Abstract
Let be a compact connected two-dimensional manifold, with or without boundary, and let
be a continuous map. We prove that if
is a minimal set of the dynamical system
then either
or M is a nowhere dense subset of
. Moreover, we add a shorter proof of the recent result of Blokh, Oversteegen and Tymchatyn, that in the former case
is a torus or a Klein bottle.
- Type
- Research Article
- Information
- Copyright
- Copyright © Cambridge University Press 2008
References
- 7
- Cited by