Parabolic type semigroups: asymptotics and order of contact

2013/09/16 by Elin, Mark, Jacobzon, Fiana
#Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1309.4002

Abstract

We study the asymptotic behavior of parabolic type semigroups acting on the unit disk as well as those acting on the right half-plane. We use the asymptotic behavior to investigate the local geometry of the semigroup trajectories near the boundary Denjoy--Wolff point. The geometric content includes, in particular, the asymptotes to trajectories, the so-called limit curvature, the order of contact, and so on. We then establish asymptotic rigidity properties for a broad class of semigroups of parabolic type.

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