Year: 2026
Type: preprint
Abstract: Let $f$ be a dominant meromorphic self-map of a compact Kähler manifold. Assume that $f$ has a strictly dominant intermediate dynamical degree $λ$ and that the number of isolated $n$-periodic points, counted with multiplicity, is at most $λ^n+o(λ^n)$. Then $f$ admits at most one adapted invariant probability measure of entropy $\logλ$. If such a measure exists, its natural extension is Bernoulli, and the isolated periodic points equidistribute towards it when counted with or without multiplicity. We apply this criterion to several classes of maps in complex dynamics, resolving longstanding open problems.
Source: arXiv (Cornell University)
Authors: Luo, Muhan, Zhou, Qi
Institution: National University of Singapore
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223120528