Topology of irrationally indifferent attractors
Dynamical Systems
2025-05-19 v5 Functional Analysis
Number Theory
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.
Keywords
Cite
@article{arxiv.1706.02678,
title = {Topology of irrationally indifferent attractors},
author = {Davoud Cheraghi},
journal= {arXiv preprint arXiv:1706.02678},
year = {2025}
}
Comments
53 pages, 10 figures. Revisions following referee reports. The original preprint under this tile is now divided into two papers. The first part of the paper on the model now appears as arXiv:2112.14557