Canonical models on strongly convex domains via the squeezing function
Amedeo Altavilla,
Leandro Arosio,
Lorenzo Guerini
Abstract:We prove that if a holomorphic self-map f : Ω → Ω of a bounded strongly convex domain Ω ⊂ C q with smooth boundary is hyperbolic then it admits a natural semi-conjugacy with a hyperbolic automorphism of a possibly lower dimensional ball B k . We also obtain the dual result for a holomorphic self-map f : Ω → Ω with a boundary repelling fixed point. Both results are obtained by rescaling the dynamics of f via the squeezing function.
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