Fixed points of commuting holomorphic mappings other than the Wolff point

被引：17

作者：

Bracci, F ^{[1
]}

机构：

[1] Univ Roma Tor Vergata, Dipartimento Matemat, I-00133 Rome, Italy

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2003年 / 355卷 / 06期

关键词：

fixed points; Wolff point; commuting mappings;

D O I：

10.1090/S0002-9947-03-03170-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let Delta be the unit disc of C and let f, g is an element of Hol(Delta, Delta) be such that f o g = g o f. For A > 1, let Fix(A)(f) := {p is an element of Delta \ lim(r-->1) f(rp) = p, lim(r-->1) \ f'(rp) \ less than or equal to A}. We study the behavior of g on Fix(A)(f). In particular, we prove that g(Fix(A)(f)) subset of or equal to Fix(A) (f). As a consequence, besides conditions for Fix(A)(f) boolean AND Fix(A)(g) not equal empty set, we prove a conjecture of C. Cowen in case f and g are univalent mappings.

引用

页码：2569 / 2584

页数：16

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