Propagation of equilibrium states in stable families of endomorphisms of ${\mathbb{P}}^k(\mathbb{C})$

Maxence Brévard, Karim Rakhimov

We prove that, within any holomorphic family of endomorphisms of ${\mathbb{P}}^k(\mathbb{C})$ in any dimension $k\ge 1$ and algebraic degree $d\ge 2$, the measurable holomorphic mo…