2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/73890This 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 $\C^n$.25 pages, 3 figuresComplex VariablesDynamical Systems32H35, 32H50, 37F99text