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

Maxence Brévard; Karim Rakhimov

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arXiv · 2405.12033

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

Maxence Brévard·Karim Rakhimov

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Abstract

We prove that, within any holomorphic family of endomorphisms of $\mathbb P^k(\mathbb C)$ in any dimension $k \geq 1$ and algebraic degree $d \geq 2$, the measurable holomorphic motion associated to dynamical stability in the sense of Berteloot-Bianchi-Dupont preserves the class of equilibrium states associated with weight functions $\psi$ satisfying $\sup\psi - \inf \psi < \log d$.

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BibTeX RIS

Maxence Brévard, Karim Rakhimov. 2024-05-20. Propagation of equilibrium states in stable families of endomorphisms of $\mathbb P^k(\mathbb C)$. https://arxiv.org/abs/2405.12033

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