Finiteness of hyperbolic entropy for holomorphic foliations with non-degenerate singularities

Abstract

Consider $\mathcal{F}=(M,\mathcal{L},E)$ a Brody-hyperbolic foliation on a compact complex surface $M$. Suppose that the singularities of $\mathcal{F}$ are all non-degenerate. We show that the hyperbolic entropy of $\mathcal{F}$ is finite.

To appear in Ann. I. Fourier

References in corpus (2)

• Ergodic theorems for laminations and foliations: recent results and perspectives
• Heat diffusions on holomorphic foliations with non-degenerate singularities