Speeds of convergence of orbits of non-elliptic semigroups of holomorphic self-maps of the unit disc

2019/07/16 by Bracci, Filippo · 3 citations
#Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1907.07098

Abstract

We introduce three quantities related to orbits of non-elliptic continuous semigroups of holomorphic self-maps of the unit disc, the total speed, the orthogonal speed and the tangential speed and show how they are related and what can be inferred from those.

Cited by

• From discrete iteration in the unit disc to continuous semigroups of holomorphic functions
• Extremal rate of convergence in discrete hyperbolic and parabolic dynamics
• Monotonicity properties of hyperbolic projections in holomorphic iteration

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• On the monotonicity of the speeds for semigroups of holomorphic self-maps of the unit disk
• On the rates of convergence of orbits in semigroups of holomorphic functions
• From discrete iteration in the unit disc to continuous semigroups of holomorphic functions