Simultaneous models for commuting holomorphic self-maps of the ball

被引：1
|
作者：
Arosio, Leandro [1 ]
Bracci, Filippo [1 ]
机构：
[1] Univ Roma Tor Vergata, Dipartimento Matemat, Via Ric Sci 1, I-00133 Rome, Italy
来源：
ADVANCES IN MATHEMATICS | 2017年 / 321卷
关键词：
Holomorphic iteration; Commuting mappings; Simultaneous linearization; Canonical models; ANALYTIC-FUNCTIONS; COMPOSITION OPERATORS; FIXED-POINTS; UNIT BALL; HYPERBOLIC AUTOMORPHISMS; SCHRODER EQUATION; ITERATION; VARIABLES; BOUNDARY;
D O I：
10.1016/j.aim.2017.10.002
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We prove that a finite family of commuting holomorphic self-maps of the unit ball B-q subset of C-q admits a simultaneous holomorphic conjugacy to a family of commuting automorphisms of a possibly lower dimensional ball, and that such conjugacy satisfies a universal property. As an application we describe when a hyperbolic and a parabolic holomorphic self-map of B-q can commute. (c) 2017 Published by Elsevier Inc.
引用
收藏
页码：486 / 512
页数：27
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