arXiv Analytics

Sign in

arXiv:1210.0179 [math.DS]AbstractReferencesReviewsResources

The Octagonal PET II: The Topology of the Limit Sets

Richard Evan Schwartz

Published 2012-09-30Version 1

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.

Comments: Following a summary of the relevant results needed from the first paper, this paper is self-contained
Categories: math.DS
Related articles: Most relevant | Search more
arXiv:1209.2390 [math.DS] (Published 2012-09-11, updated 2012-09-30)
The Octagonal PET I: Renormalization and Hyperbolic Symmetry
arXiv:1601.04906 [math.DS] (Published 2016-01-19)
Structure of $ω$-limit Sets for Almost-periodic Parabolic Equations on $S^1$ with Reflection Symmetry
arXiv:2203.06794 [math.DS] (Published 2022-03-14)
Dichotomy and measures on limit sets of Anosov groups

Links

Toolbox