On Valiron's Theorem

2003/10/28 by Filippo Bracci, Bracci, Filippo, Pietro Poggi-Corradini +1 · 2 citations
Mathematics · #30D05 #Complex Variables (math.CV) #FOS: Mathematics #math.CV #msc:30D05

paper · pdf · doi:10.48550/arxiv.math/0310440

20 pages

arxiv created 2003/10/28 · arxiv updated 2009/12/01

Abstract

This is a survey on Valiron's Theorem about the convergence properties of orbits of analytic self-maps of the disk of hyperbolic type and related questions in one and several variables.

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

Related

• Valiron and Abel equations for holomorphic self-maps of the polydisc
• Valiron's construction in higher dimension
• Parabolic dynamics according to Maurice Heins
• Backward-iteration sequences with bounded hyperbolic steps for analytic self-maps of the disk
• Extremal rate of convergence in discrete hyperbolic and parabolic dynamics