Topology of irrationally indifferent attractors

2017/06/08 by Cheraghi, Davoud · 1 citation
#37F10 #37F50 (Primary) #46T25 (Secondary) #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Analysis (math.FA) #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1706.02678

Abstract

We study the post-critical set of a class of holomorphic systems with an irrationally indifferent fixed point. We prove a trichotomy for the topology of the post-critical set based on the arithmetic of the rotation number at the fixed point. The only options are Jordan curves, a one-sided hairy Jordan curves, and Cantor bouquet. This explains the degeneration of the closed invariant curves inside the Siegel disks, as one varies the rotation number.

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