Year: 2021
Type: article
Abstract: Let $f : X\to X$ be a dominating meromorphic map on a compact Kähler manifold $X$ of dimension $k$. We extend the notion of topological entropy $h^l_{\mathrm{top}}(f)$ for the action of $f$ on (local) analytic sets of dimension $0\leq l \leq k$. For an ergodic probability measure $ν$, we extend similarly the notion of measure-theoretic entropy $h_ν^l(f)$. Under mild hypothesis, we compute $h^l_{\mathrm{top}}(f)$ in term of the dynamical degrees of $f$. In the particular case of endomorphisms of $\mathbb{P}^2$ of degree $d$, we show that $h^1_{\mathrm{top}}(f)= \log d$ for a large class of maps but we give examples where $h^1_{\mathrm{top}}(f)\neq \log d$.
Authors: Henry De Thelin, Gabriel Vigny
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Agence Nationale de la Recherche
OpenAlex ID: W2883979247