Maximal Entropy Measures for Non-accessible Topological Skew Products

Cubas Becerra R.J.; Tahzibi A. · Bulletin of the Brazilian Mathematical Society (2026) · DOI: 10.1007/s00574-026-00512-8

Resumen

In this paper, we establish a dichotomy for ergodic measures of maximal entropy of partially hyperbolic diffeomorphisms with compact one-dimensional center leaves that are virtually skew products over a transitive Anosov homeomorphism. We prove that if the whole manifold is the unique minimal invariant set saturated by the unstable foliation, then exactly one of the following holds: either there exists a unique non-hyperbolic measure of maximal entropy, or there exist exactly two ergodic measures of maximal entropy, both hyperbolic, with center Lyapunov exponents of opposite signs. © The Author(s), under exclusive licence to Brazilian Mathematical Society 2026.

Instituciones: Universidad Científica del Sur