Article contents
Positive topological entropy for monotone recurrence relations
Published online by Cambridge University Press: 30 June 2014
Abstract
We associate the topological entropy of monotone recurrence relations with the Aubry–Mather theory. If there exists an interval $[{\it\rho}_{0},{\it\rho}_{1}]$ such that, for each ${\it\omega}\in ({\it\rho}_{0},{\it\rho}_{1})$, all Birkhoff minimizers with rotation number ${\it\omega}$ do not form a foliation, then the diffeomorphism on the high-dimensional cylinder defined via the monotone recurrence relation has positive topological entropy.
- Type
- Research Article
- Information
- Copyright
- © Cambridge University Press, 2014
References
- 4
- Cited by