Duke Mathematical Journal

Laminar currents and birational dynamics

Romain Dujardin

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Abstract

We study the dynamics of a bimeromorphic map $X\rightarrow X$, where $X$ is a compact complex Kähler surface. 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

Article information

Source
Duke Math. J. Volume 131, Number 2 (2006), 219-247.

Dates
First available in Project Euclid: 12 January 2006

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1137077884

Digital Object Identifier
doi:10.1215/S0012-7094-06-13122-8

Mathematical Reviews number (MathSciNet)
MR2219241

Zentralblatt MATH identifier
1099.37037

Subjects
Primary: 37F10: Polynomials; rational maps; entire and meromorphic functions [See also 32A10, 32A20, 32H02, 32H04] 32H50: Iteration problems 32U40: Currents

Citation

Dujardin, Romain. Laminar currents and birational dynamics. Duke Mathematical Journal 131 (2006), no. 2, 219--247. doi:10.1215/S0012-7094-06-13122-8. http://projecteuclid.org/euclid.dmj/1137077884.


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