Canonical Models on Strongly Convex Domains via the Squeezing Function

被引：3

作者：

Altavilla, Amedeo ^{[1
]}

Arosio, Leandro ^{[2
]}

Guerini, Lorenzo ^{[3
]}

机构：

[1] Univ Bari Aldo Moro, Dipartimento Matemat, Via E Orabona 4, I-70125 Bari, Italy

[2] Univ Roma Tor Vergata, Dipartimento Matemat, Via Ric Sci 1, I-00133 Rome, Italy

[3] Univ Amsterdam, Korteweg de Vries Inst Math, Sci Pk 107, NL-1090 GE Amsterdam, Netherlands

来源：

JOURNAL OF GEOMETRIC ANALYSIS | 2021年 / 31卷 / 05期

关键词：

Strongly convex domains; Iteration theory; Squeezing function; Canonical models; BACKWARD ITERATION; FIXED-POINTS; MAPPINGS;

D O I：

10.1007/s12220-020-00448-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that if a holomorphic self-map f: Omega ->Omega of a bounded strongly convex domain Omega subset of C-q with smooth boundary is hyperbolic then it admits a natural semi-conjugacy with a hyperbolic automorphism of a possibly lower dimensional ball Bk. We also obtain the dual result for a holomorphic self-map f : Omega ->Omega with a boundary repelling fixed point. Both results are obtained by rescaling the dynamics of f via the squeezing function.

引用

页码：4661 / 4702

页数：42

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