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A local study near the Wolff point on the ball

Part of: Holomorphic mappings and correspondences Pseudoconvex domains

Published online by Cambridge University Press:  17 June 2020

Fengbai Li  and
Feng Rong
Fengbai Li
Affiliation:
School of Mathematics, Shanghai University of Finance and Economics, 777 Guo Ding Road, Shanghai200433, P.R. China ([email protected])
Feng Rong
Affiliation:
School of Mathematical Sciences, Shanghai Jiao Tong University, 800 Dong Chuan Road, Shanghai200240, P.R. China ([email protected])
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Abstract

Let f be a holomorphic self-map of the unit ball in dimension 2, which does not have an interior fixed point. Suppose that f has a Wolff point p with the boundary dilatation coefficient equal to 1 and the non-tangential differential dfp = id. The local behaviours of f near p are quite diverse, and we give a detailed study in many typical cases. As a byproduct, we give a dynamical interpretation of the Burns–Krantz rigidity theorem. Note also that similar results hold on two-dimensional contractible smoothly bounded strongly pseudoconvex domains.

Keywords

Wolff pointSiegel upper half-planeholomorphic self-map

MSC classification

Primary: 32H50: Iteration problems
Secondary: 32T15: Strongly pseudoconvex domains
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 63 , Issue 3 , August 2020 , pp. 761 - 779
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Copyright
Copyright © The Authors, 2020. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society

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