Boundary behavior and rigidity of semigroups of holomorphic mappings
Mark Elin, David Shoikhet
TL;DR
This paper investigates the boundary behavior of semigroups of holomorphic self-mappings of the unit disk, focusing on their asymptotic properties and establishing rigidity results for parabolic types.
Contribution
It introduces quantitative measures of boundary asymptotics and proves an asymptotic rigidity property for semigroups of parabolic type.
Findings
Quantitative characteristics of boundary asymptotic behavior
Limit curvature of trajectories at the Denjoy--Wolff point
Asymptotic rigidity property for parabolic semigroups
Abstract
In this paper we give some quantative characteristics of boundary asymptotic behavior of semigroups of holomorphic self-mappings of the unit disk including the limit curvature of their trajectories at the boundary Denjoy--Wolff point. This enable us to establish an asymptotic rigidity property for semigroups of parabolic type.
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Taxonomy
TopicsHolomorphic and Operator Theory · Analytic and geometric function theory · Geometric and Algebraic Topology