Finite Measures of Maximal Entropy for an Open Set of Partially Hyperbolic Diffeomorphisms
Dynamical Systems
2024-05-09 v3
Abstract
We consider partially hyperbolic diffeomorphisms with a one-dimensional central direction such that the unstable entropy exceeds the stable entropy. Our main result proves that such maps have a finite number of ergodic measures of maximal entropy. Moreover, any diffeomorphism near in the topology possesses at most the same number of ergodic measures of maximal entropy. Our contribution is in extending the findings in [4] to arbitrary dimensions. We believe our technique, essentially distinct from the one in that paper, is robust and may find applications in further contexts.
Keywords
Cite
@article{arxiv.2401.02776,
title = {Finite Measures of Maximal Entropy for an Open Set of Partially Hyperbolic Diffeomorphisms},
author = {Juan Carlos Mongez and Maria Jose Pacifico},
journal= {arXiv preprint arXiv:2401.02776},
year = {2024}
}