Ergodic Theory and Dynamical Systems· 2026Q1
Hyperbolic foliated entropy of suspensions
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- 2026year
Short summary
A new link is established between the hyperbolic entropies of foliations obtained by suspensions and an adapted Ghys, Langevin, and Walczak entropy for pseudo-groups, implying non-invariance by diffeomorphisms and admitting an invariant measure for minimal entropy suspensions.
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Key points
- Establishes a link between hyperbolic entropies of foliations (via suspensions) and adapted Ghys, Langevin, Walczak entropy for pseudo-groups.
- Demonstrates that hyperbolic entropy of foliations is not invariant by diffeomorphisms.
- Proves that minimal entropy suspensions admit an invariant measure.
- Provides the first exact estimate of hyperbolic entropy for representations isomorphic to Z, along with Brin-Katok-type and variational principles.
AI-generated from the title and abstract; the full text is not read.
Abstract
Abstract 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 $\mathbb {Z}$ double struck upper 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.
The authors' abstract, as published at the source. Ergodic Theory and Dynamical Systems, 2026 · DOI ↗
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Field: Mathematical Physics
Mathematical PhysicsMathematics