The Octagonal PET II: The Topology of the Limit Sets
Dynamical Systems
2012-10-02 v1
Abstract
This is a sequel to my paper "The Octagonal PET I: Renormalization and Hyperbolic Symmetry". In this paper we use the renormalization scheme found in the first paper to classify the limit sets of the systems according to their topology. The main result is that the limit set is either a finite forest or a Cantor set, with an explicit description of which cases occur for which parameters. In one special case, the limit set is a disjoint union of 2 arcs if and only if the continued fraction expansion of the parameter has the form [a0:a1:a2:a3...] with a_k even for every odd k.
Keywords
Cite
@article{arxiv.1210.0179,
title = {The Octagonal PET II: The Topology of the Limit Sets},
author = {Richard Evan Schwartz},
journal= {arXiv preprint arXiv:1210.0179},
year = {2012}
}
Comments
Following a summary of the relevant results needed from the first paper, this paper is self-contained