Dynamique des applications holomorphes propres de domaines reguliers et probleme de l'injectivite

Details Dynamique des applications holomorphes propres de domaines reguliers et probleme de l'injectivite Dynamique des applications holomorphes propres de domaines reguliers et probleme de l'injectivite

2005-01-19

arxiv.org/abs/math/0501293v1

Mathematics

Complex Variables

25 pages, 3 figures

Scientific paper

This paper deals with proper holomorphic self-maps of smoothly bounded pseudoconvex domains in $\C^2$. We study the dynamical properties of their extension to the boundary and show that their non-wandering sets are always contained in the weakly pseudoconvex part of the boundary. In the case of complete circular domains, we combine this fact with an entropy/degree argument to show that the maps are automorphisms. Some of our results remain true in $\C^n$.

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