Article contents
Maximal entropy measures for piecewise affine surface homeomorphisms
Published online by Cambridge University Press: 21 May 2009
Abstract
We study the dynamics of piecewise affine surface homeomorphisms from the point of view of their entropy. Under the assumption of positive topological entropy, we establish the existence of finitely many ergodic and invariant probability measures maximizing entropy and prove a multiplicative lower bound for the number of periodic points. This is intended as a step towards the understanding of surface diffeomorphisms. We proceed by building a jump transformation, using not first returns but carefully selected ‘good’ returns to dispense with Markov partitions. We control these good returns through some entropy and ergodic arguments.
- Type
- Research Article
- Information
- Copyright
- Copyright © Cambridge University Press 2009
References
- 12
- Cited by