Laminar currents and birational dynamics

Romain Dujardin

Laminar currents and birational dynamics

动力系统 2007-05-23 v2 复变函数

作者: Romain Dujardin

摘要

We study the dynamics of a bimeromorphic selfmap of a compact complex K\"ahler surface $X$ . Under a natural geometric hypothesis, we construct an invariant probability measure, which is mixing, hyperbolic and of maximal entropy. The proof relies heavily on the theory of laminar currents and is new even in the case of polynomial automorphisms of $\mathbb{C}^2$ . This extends recent results by E. Bedford and J. Diller.

关键词

holomorphic dynamics dynamical systems and chaos kähler manifolds

引用

@article{arxiv.math/0409557,
  title  = {Laminar currents and birational dynamics},
  author = {Romain Dujardin},
  journal= {arXiv preprint arXiv:math/0409557},
  year   = {2007}
}

备注

Added more preliminaries on laminar currents and other minor corrections. To appear in Duke Math. J

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