Une caractérisation des endomorphismes de Lattès par leur mesure de Green

By F. Berteloot, C. Dupont. 2005

46 citations recorded by the source corpus.

We show that the Lattes endomorphisms are the only holomorphic endomorphisms of the complex $k$-dimensional projective space whose measure of maximal entropy is absolutely continuous with respect to the Lebesgue measure. As a consequence, Lattes endomorphisms are also characterized by other extremal properties as the maximality of the Hausdorff dimension of their measure of maximal entropy or the minimality of their Liapounov exponents. Our proof uses a linearization method which is of independant interest and a previous characterization by the regularity of the Green current.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c58e5940e19938de844a586d2bf40da987a55516

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Normalization of bundle holomorphic contractions and applications to dynamics (2007, methodology): “A weak version of it, corresponding to the case where all Lyapunov exponents are equal, has been used in [4] for characterizing the endomorphisms f for which μ is absolutely continuous with respect to the Lebesgue measure.”
Dynamics in Several Complex Variables: Endomorphisms of Projective Spaces and Polynomial-like Mappings (2008, methodology): “We refer to [10, 12, 37, 45, 103] for a discussion of Lattès maps.”