Grand orbit relations in wandering domains

2024/05/24 by Evdoridou, Vasiliki, Fagella, Núria, Geyer, Lukas +1 · 2 citations
#Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2405.15667

Abstract

One of the fundamental distinctions in McMullen and Sullivan's description of the Teichmüller space of a complex dynamical system is between discrete and indiscrete grand orbit relations. We investigate these on the Fatou set of transcendental entire maps and provide criteria to distinguish between the two types. Furthermore, we show that discrete and indiscrete grand orbit relations may coexist non-trivially in a wandering domain, a phenomenon which does not occur for any other type of Fatou component. One of the tools used is a novel quasiconformal surgery technique of independent interest.

Cited by

• Baker domains and orbits disappearing to infinity
• Teichmüller spaces and normal forms associated to wandering domains

Related

• Teichmüller spaces and normal forms associated to wandering domains
• Wandering domains with nearly bounded orbits
• Holomorphic motions, natural families of entire maps, and multiplier-like objects for wandering domains
• Wandering domains for composition of entire functions
• A new family of entire functions with no wandering domains