Topological Rigidity of good fractal necklaces
Dynamical Systems
2021-10-14 v3 General Topology
Abstract
We introduce and characterize extremal 2-cuts for good fractal necklaces. Using the characterization and the related topological properties of extremal 2-cuts, we prove that every good necklace has a unique necklace IFS in a certain sense. Also, we prove that two good necklaces admit only rigid homeomorphisms and thus the group of self-homeomorphisms of a good necklace is countable. In addition, a certain weaker co-Hopfian property of good necklaces is also obtained.
Keywords
Cite
@article{arxiv.2105.01318,
title = {Topological Rigidity of good fractal necklaces},
author = {Fan Wen},
journal= {arXiv preprint arXiv:2105.01318},
year = {2021}
}