Strong probabilistic stability in holomorphic families of endomorphisms of ${\mathbb{P}}^k(\mathbb{C})$ and polynomial-like maps

Fabrizio Bianchi, Karim Rakhimov

We prove that, in stable families of endomorphisms of ${\mathbb{P}}^k(\mathbb{C})$, all invariant measures whose measure-theoretic entropy is strictly larger than $(k-1)\log d$ at a…