[CvGmt News] Seminario di sistemi dinamici (olomorfi e dintorni)
Marco Abate
abate at dm.unipi.it
Fri Apr 25 18:09:21 CEST 2003
SEMINARIO DI SISTEMI DINAMICI (olomorfi e dintorni)
Aula Seminari del Centro di Ricerca Matematica Ennio De Giorgi
Piazza dei Cavalieri, Collegio Puteano
Martedi' 29 aprile ore 14:30
Prof. Francois BERTELOOT, Universite de Toulouse
A characterization of Lattes endomorphisms by their
maximal entropy measure
Abstract : The Lattes endomorphisms are induced on the $k$-dimensional
projective complex space
by a dilation of a complex torus. These endomorphisms are characterized
by one of the following properties of their maximal entropy measure
$\mu$ :
1) $\mu$ is absolutely continuous with respect to the Lebesgue measure
2) all Liapounov exponents of $\mu$ are minimal
3) the Hausdorff dimension of $\mu$ is maximal.
We shall explain how these conditions are related and describe the main
steps of the proof of the characterization. One important tool,
which we shall discuss, is a linearization procedure
along typical orbits for general endomorphisms. It allows to relate the
regularity of $\mu$ and the regularity of the Green current $T$
($\mu$ is a power of $T$ in the Bedford-Taylor sense).
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