Laminar currents and birational dynamics

By Romain Dujardin. 2004

80 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c9c68d1a290abbd4b8a01b545a7f119fb4d7f011

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In Applied Mathematics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Dynamics on blowups of the projective plane (2007, background): “For more on the maximal measure, see [BD], [ Duj ] and references therein.”
Dynamics of meromorphic maps with small topological degree III: geometric currents and ergodic theory (2008, methodology): “We can now compute the entropy, using the Rokhlin formula and the invariant “Pesin partition” of [LS], as in [ Du4 ].”
Periodicities in linear fractional recurrences: Degree growth of birational surface maps (2005, background): “[ D2 ] showed that this invariant measure may be found by taking the “geometric intersection” of the measured laminations Ls and Lu.”
Equidistribution problems of complex dynamics in higher dimension (2016, background): “For the construction of a good family of periodic points, see Dujardin [39].”
Dynamics of automorphisms of compact complex surfaces (2014, background): “13), it can be shown that (see [10, 34, 66]) (1) Pesin boxes provide a complete family of flow boxes for T + f ; in other words, T + f is a sum of T + f |Ks over a family of Pesin boxes;”