Measure of maximal entropy for H-flows on non-compact manifolds
Dynamical Systems
2025-12-05 v1
Abstract
In this work, we introduce a natural class of chaotic flows on non-compact manifolds, called H-flows, which includes geodesic flows on non-compact manifolds with pinched negative curvature. We show that, under the additional assumption, called strong positive recurrence, that their entropy at infinity is strictly smaller than the topological entropy, such flows admit an invariant probability measure maximizing entropy. In particular, we compare several notions of entropy in a non-compact setting.
Cite
@article{arxiv.2512.04657,
title = {Measure of maximal entropy for H-flows on non-compact manifolds},
author = {Anna Florio and Barbara Schapira and Anne Vaugon},
journal= {arXiv preprint arXiv:2512.04657},
year = {2025}
}