English

On weak separation property for self-affine Jordan arcs

Metric Geometry 2020-06-24 v1 Geometric Topology

Abstract

We consider self-affine arcs in R2\mathbb R^2 and prove that violation of "inner" weak separation property for such arcs implies that the arc is a parabolic segment. Therefore, if a self-affine Jordan arc is not a parabolic segment, then it is the attractor of some multizipper.

Cite

@article{arxiv.2006.13199,
  title  = {On weak separation property for self-affine Jordan arcs},
  author = {Andrei Tetenov and Olesya Chelkanova},
  journal= {arXiv preprint arXiv:2006.13199},
  year   = {2020}
}
R2 v1 2026-06-23T16:33:55.327Z