Hyperbolic foliated entropy of suspensions
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912756804878336 |
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| author | Bacher, François |
| author_facet | Bacher, François |
| contents | 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~$\mathbb{Z}$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_09528 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hyperbolic foliated entropy of suspensions Bacher, François Dynamical Systems Complex Variables 37F75, 37A15, 37B40, 22D40 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~$\mathbb{Z}$. 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. |
| title | Hyperbolic foliated entropy of suspensions |
| topic | Dynamical Systems Complex Variables 37F75, 37A15, 37B40, 22D40 |
| url | https://arxiv.org/abs/2512.09528 |