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Variational principle for the Carathéodory--Pesin entropy of foliations

  • Andrzej Biś
  • Maria Carvalho
  • Paulo Varandas
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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.

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Cite

BibTeXRIS
BibTeX
@misc{bis2026variational,
  title = {{Variational principle for the Carathéodory--Pesin entropy of foliations}},
  author = {Andrzej Biś and Maria Carvalho and Paulo Varandas},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.34557},
  eprint = {2610.34557},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.34557},
}
RIS
TY  - UNPB
TI  - Variational principle for the Carathéodory--Pesin entropy of foliations
AU  - Andrzej Biś
AU  - Maria Carvalho
AU  - Paulo Varandas
PY  - 2026
DA  - 2026/10/25
PB  - arXiv
DO  - 10.48550/arxiv.2610.34557
UR  - https://arxiv.org/abs/2610.34557
AB  - 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.
ER  -