October 13, 2025Open Access

C⁰-Contact Anosov flows

Key Points

Smooth reparametrizations of geodesic flow are shown to be contact Anosov flows, expanding the understanding of dynamical systems.
The introduction of the $C^0$-contact notion leads to a class of exponentially mixing Anosov flows, highlighting its importance.
The classical Gray stability theorem fails in this $C^0$-contact context, indicating significant differences from the smooth case.
This work opens up new avenues for studying the stability of contact Anosov flows in various manifold settings.

Abstract

We prove that smooth reparametrizations of the geodesic flow on a manifold of constant negative curvature are contact Anosov flows. In particular we give a new class of exponentially mixing Anosov flows. Moreover, this introduces the notion of C⁰-contact and we prove that the classical Gray stability theorem that is known in the smooth case fails in this setting.

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Cite This Study

Khoule et al. (Sat,) studied this question.

synapsesocial.com/papers/68ecc715d1cc7436f7d18a4d https://doi.org/https://doi.org/10.48550/arxiv.2503.00454

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