Propagation of equilibrium states in stable families of endomorphisms of $\mathbb P^k(\mathbb C)$
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911882120527872 |
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| author | Brévard, Maxence Rakhimov, Karim |
| author_facet | Brévard, Maxence Rakhimov, Karim |
| contents | 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 $ψ$ satisfying $\supψ- \inf ψ< \log d$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_12033 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Propagation of equilibrium states in stable families of endomorphisms of $\mathbb P^k(\mathbb C)$ Brévard, Maxence Rakhimov, Karim Dynamical Systems 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 $ψ$ satisfying $\supψ- \inf ψ< \log d$. |
| title | Propagation of equilibrium states in stable families of endomorphisms of $\mathbb P^k(\mathbb C)$ |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2405.12033 |