Laminar currents and birational dynamics

Details Laminar currents and birational dynamics Laminar currents and birational dynamics

2004-09-28

arxiv.org/abs/math/0409557v2

Mathematics

Dynamical Systems

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

Scientific paper

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.

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