Work

Variational principle for the Carathéodory--Pesin entropy of foliations

Year: 2026

Type: preprint

Abstract: We introduce Carathéodory-Pesin structures for non-singular foliations on Riemannian manifolds and define a new notion of entropy for such foliations. Under dynamical and geometric assumptions on the corresponding holonomy pseudogroups, we establish a variational description of this new concept which relates it to the local metric entropy of measures on transversals and to the entropy of harmonic measures on the manifold.

Source: arXiv (Cornell University)

DOI: 10.13140/rg.2.2.17236.77445

Authors: Andrzej Biś, Maria Carvalho, Paulo Varandas

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Uniwersytet Łódzki, Center for Research and Development in Mathematics and Applications, Fundação para a Ciência e a Tecnologia, Centro de Matemática Universidade do Porto

Awards: Centro de Matemática da Universidade do Porto, G253191505, G2585177937, G307494477, G3659559413, G3929736893, G7851690062, G8511605407, G9001166219

OpenAlex ID: W7223577876

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