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- W2177729663 abstract "We introduce a notion of hyperbolicity and parabolicity for a holomorphic self-map $f: Delta^N to Delta^N$ of the polydisc which does not admit fixed points in $Delta^N$. We generalize to the polydisc two classical one-variable results: we solve the Valiron equation for a hyperbolic $f$ and the Abel equation for a parabolic nonzero-step $f$. This is done by studying the canonical Kobayashi hyperbolic semi-model of $f$ and by obtaining a normal form for the automorphisms of the polydisc. In the case of the Valiron equation we also describe the space of all solutions." @default.
- W2177729663 created "2016-06-24" @default.
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- W2177729663 date "2015-09-14" @default.
- W2177729663 modified "2023-09-27" @default.
- W2177729663 title "Valiron and Abel equations for holomorphic self-maps of the polydisc" @default.
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