2025/12/10 by François Bacher, Bacher, François
Mathematics · Physics and Astronomy · #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #math.CV #math.DS
paper · pdf · doi:10.48550/arxiv.2512.09528
openalex publication_date 2025/12/10 · openalex created_date 2025/12/12 · openalex updated_date 2026/07/28
We study the hyperbolic entropies of foliations obtained by suspensions of a representation, in the sense of Dinh, Nguyên and Sibony (topological and measure-theoretic). We establish a link between this type of entropy and an adapted version of an entropy defined by Ghys, Langevin and Walczak for pseudo-groups of homeomorphisms. Such a link has various consequences. Among them, it implies that the hyperbolic entropy of foliations is not invariant by diffeomorphisms, and that a minimal entropy suspension admits an invariant measure. Finally, this allows us to study thoroughly the simple case in which the image of the representation is isomorphic to~ℤ. In that case, we give the first exact estimate of the hyperbolic entropy, and prove a Brin--Katok type theorem and a variational principle, relying strongly on the standard ones for the entropy of maps.