For a non-generic, yet dense subset of C1 expanding Markov maps of the interval we prove the existence of uncountably many Lyapunov optimizing measures which are ergodic, fully supported and have positive entropy. These measures are equilibrium states for some Hölder continuous potentials. We also prove the existence of another non-generic dense subset for which the optimizing measure is unique and supported on a periodic orbit. A key ingredient is a new C1 perturbation lemma which allows us to interpolate between expanding Markov maps and the shift map on a finite number of symbols.
37A40, 37C40, 37D05, 37D35, 37E05.
37A40, 37C40, 37D05, 37D35, 37E05
|Publication status||Published - 2017 May 22|
- Expanding Markov map
- Lyapunov optimizing measure
- Non-generic property
ASJC Scopus subject areas