Unique ergodicity for singular holomorphic foliations of $\mathbb{P}^3(\mathbb{C})$ with an invariant plane

Abstract

We prove a unique ergodicity theorem for singular holomorphic foliations of $\mathbb{P}^3(\mathbb{C})$ with hyperbolic singularities and with an invariant plane with no foliation cycle, in analogy with a result of Dinh-Sibony concerning unique ergodicity for foliations of $\mathbb{P}^2(\mathbb{C})$ with an invariant line. The proof is dynamical in nature and adapts the work of Deroin-Kleptsyn to a singular context, using the fundamental integrability estimate of Nguy\^en.