Measure of maximal entropy for H-flows on non-compact manifolds

2025/12/04 by Florio, Anna, Schapira, Barbara, Vaugon, Anne
Mathematics · Physics and Astronomy · #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #Geometric Analysis and Curvature Flows

paper · doi:10.48550/arxiv.2512.04657

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.

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