Canonical Models on Strongly Convex Domains via the Squeezing Function

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...

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Veröffentlicht in:	The Journal of Geometric Analysis 2021-05, Vol.31 (5), p.4661-4702
Hauptverfasser:	Altavilla, Amedeo, Arosio, Leandro, Guerini, Lorenzo
Format:	Artikel
Sprache:	eng
Schlagworte:	Abstract Harmonic Analysis Automorphisms Compressing Convex and Discrete Geometry Differential Geometry Domains Dynamical Systems and Ergodic Theory Fourier Analysis Geometry Global Analysis and Analysis on Manifolds Mathematical analysis Mathematics Mathematics and Statistics Rescaling Smooth boundaries
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creator	Altavilla, Amedeo Arosio, Leandro Guerini, Lorenzo
description	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.
doi_str_mv	10.1007/s12220-020-00448-5
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subjects	Abstract Harmonic Analysis Automorphisms Compressing Convex and Discrete Geometry Differential Geometry Domains Dynamical Systems and Ergodic Theory Fourier Analysis Geometry Global Analysis and Analysis on Manifolds Mathematical analysis Mathematics Mathematics and Statistics Rescaling Smooth boundaries
title	Canonical Models on Strongly Convex Domains via the Squeezing Function
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