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

Félix Lequen

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

Dynamical Systems 2025-01-20 v2 Complex Variables

Authors: Félix Lequen

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.

Keywords

unique ergodicity holomorphic foliations invariant plane hyperbolic singularities dynamical proof

Cite

@article{arxiv.2212.01531,
  title  = {Unique ergodicity for singular holomorphic foliations of $\mathbb{P}^3(\mathbb{C})$ with an invariant plane},
  author = {Félix Lequen},
  journal= {arXiv preprint arXiv:2212.01531},
  year   = {2025}
}

Comments

51 pages; major revision, many typos fixed, a gap was filled in the proof, much more details, slight extension of results

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

Abstract

Keywords

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