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Measures of maximal entropy for meromorphic maps on compact Kähler manifolds

  • Muhan Luo
  • Qi Zhou
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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 λn+o(λn). 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.

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Cite

BibTeXRIS
BibTeX
@misc{luo2026measures,
  title = {{Measures of maximal entropy for meromorphic maps on compact Kähler manifolds}},
  author = {Muhan Luo and Qi Zhou},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.28617},
  eprint = {2610.28617},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.28617},
}
RIS
TY  - UNPB
TI  - Measures of maximal entropy for meromorphic maps on compact Kähler manifolds
AU  - Muhan Luo
AU  - Qi Zhou
PY  - 2026
DA  - 2026/10/24
PB  - arXiv
DO  - 10.48550/arxiv.2610.28617
UR  - https://arxiv.org/abs/2610.28617
AB  - 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.
ER  -