Titre :

HYPERBOLIC ENTROPY FOR HARMONIC MEASURES ON SINGULAR HOLOMORPHIC FOLIATIONS

Auteur(s) :

Bacher, François [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Date de publication :

2024-10-25

Mot(s)-clé(s) en anglais :

Singular holomorphic foliation
Hyperbolic entropy
Ergodic Theory
Poincaré metric
Harmonic measures

Discipline(s) HAL :

Mathématiques [math]

Résumé en anglais : [en]

<div><p>Let F " pM, L , Eq be a Brody-hyperbolic singular holomorphic foliation on a compact complex manifold M . Suppose that F has isolated singularities and that its Poincaré metric is complete. This is the case for a ...
Lire la suite ><div><p>Let F " pM, L , Eq be a Brody-hyperbolic singular holomorphic foliation on a compact complex manifold M . Suppose that F has isolated singularities and that its Poincaré metric is complete. This is the case for a very large class of singularities, namely, non-degenerate and saddle-nodes in dimension 2. Let µ be an ergodic harmonic measure on F . We show that the upper and lower local hyperbolic entropies of µ are leafwise constant almost everywhere. Moreover, we show that the entropy of µ is at least 2.</p></div>Lire moins >

Langue :

Anglais

Projet ANR :

Quantisation, singularités et dynamique holomorphe

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Date de dépôt :

2024-11-07T09:02:14Z