Quasisymmetries of Sierpi\'nski carpet Julia sets
Dynamical Systems
2014-03-04 v1
Abstract
We prove that if is a quasisymmetric homeomorphism between Sierpi\'nski carpets that are the Julia sets of postcritically-finite rational maps, then is the restriction of a M\"obius transformation to the Julia set. This implies that the group of quasisymmetric homeomorphisms of a Sierpi\'nski carpet Julia set of a postcritically-finite rational map is finite.
Keywords
Cite
@article{arxiv.1403.0392,
title = {Quasisymmetries of Sierpi\'nski carpet Julia sets},
author = {Mario Bonk and Misha Lyubich and Sergei Merenkov},
journal= {arXiv preprint arXiv:1403.0392},
year = {2014}
}