On the measures of large entropy on a positive closed current

Abstract

Let $f:X\to X$ be a dominating meromorphic map of a compact Kähler surface of large topological degree. Let $S$ be a positive closed current on $X$ of bidegree $(1,1)$. We consider an ergodic measure $\nu$ of large entropy supported by $\mathrm{supp}(S)$. Defining dimensions for $\nu$ and $S$, we give inequalities à la Mañé involving the Lyapunov exponents of $\nu$ and those dimensions. We give dynamical applications of those inequalities.

34 pages

References in corpus (1)

• Dynamics in several complex variables: endomorphisms of projective spaces and polynomial-like mapping