Title :

HYPERBOLIC ENTROPY FOR HARMONIC MEASURES ON SINGULAR HOLOMORPHIC FOLIATIONS

Author(s) :

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

Publication date :

2024-10-25

English keyword(s) :

Singular holomorphic foliation
Hyperbolic entropy
Ergodic Theory
Poincaré metric
Harmonic measures

HAL domain(s) :

Mathématiques [math]

English abstract : [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 ...
Show more ><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>Show less >

Language :

Anglais

ANR Project :

Quantisation, singularités et dynamique holomorphe

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Submission date :

2024-11-07T09:02:14Z