On commuting holomorphic maps in the unit disc of
作者:
Fabio Vlacci,
期刊:
Complex Variables, Theory and Application: An International Journal
(Taylor Available online 1996)
卷期:
Volume 30,
issue 4
页码: 301-131
ISSN:0278-1077
年代: 1996
DOI:10.1080/17476939608814932
出版商: Gordon and Breach Science Publishers
关键词: 32H50;32A40
数据来源: Taylor
摘要:
A connection between the study of commuting holomorphic maps of the unit disc Δ ofinto itself and the study of holomorphic maps of Δ into itself that belong to the same pseudo-iteration semigroup (in the sense of Cowen) is investigated. The open (and difficult) case in which the maps have derivative 1 at the Wolff point τ ∂ ε Δ is considered in this paper. Among other results, it is proved that the set of all holomorphic maps of the unit disc Δ into itself which commute with a given holomorphic mapfcoincides with the set of all holomorphic maps which belong to the pseudo-iteration semigroup off. The results are obtained under the hypothesis—which appears naturally in the context—that the iterates of the involved maps converge to the (common) Wolff point “non-tangentially”.
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