Laplacians on Julia sets of rational maps
Dynamical Systems
2020-01-14 v1 Functional Analysis
Abstract
The study of Julia sets gives a new and natural way to look at fractals. When mathematicians investigated the special class of Misiurewicz's rational maps, they found out that there is a Julia set which is homeomorphic to a well known fractal, the Sierpinski gasket. In this paper, we apply the method of Kigami to give rise to a new construction of Laplacians on the Sierpinski gasket like Julia sets with a dynamically invariant property.
Cite
@article{arxiv.2001.03821,
title = {Laplacians on Julia sets of rational maps},
author = {Malte S. Hassler and Hua Qiu and Robert S. Strichartz},
journal= {arXiv preprint arXiv:2001.03821},
year = {2020}
}
Comments
15 pages, 8 figures