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

Emmanuel Opshtein
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Abstract

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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Emmanuel Opshtein. 2005-01-19. Dynamique des applications holomorphes propres de domaines reguliers et probleme de l'injectivite. https://arxiv.org/abs/math/0501293

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