In this survey we give geometric interpretations of some standard results on boundary behaviour of holomorphic self-maps in the unit disc of ℂ and generalize them to holomorphic self-maps of some particular domains of ℂⁿ.
A connection between iteration theory and the study of sets of commuting holomorphic maps is investigated, in the unit disc of . In particular, given two holomorphic maps and of the unit disc into itself, it is proved that if belongs to the pseudo-iteration semigroup of (in the sense of Cowen) then - under certain conditions on the behaviour of their iterates - the maps and commute.
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