Self-similar Dirichlet forms on polygon carpets
Dynamical Systems
2022-06-02 v1 Functional Analysis
Probability
Abstract
We construct symmetric self-similar diffusions with sub-Gaussian heat kernel estimates on two types of polygon carpets, which are natural generalizations of planner Sierpinski carpets (SC). The first ones are called perfect polygon carpets that are natural analogs of SC in that any intersection cells are either side-to-side or point-to-point. The second ones are called bordered polygon carpets which satisfy the boundary including condition as SC but allow distinct contraction ratios.
Cite
@article{arxiv.2206.00040,
title = {Self-similar Dirichlet forms on polygon carpets},
author = {Shiping Cao and Hua Qiu and Yizhou Wang},
journal= {arXiv preprint arXiv:2206.00040},
year = {2022}
}
Comments
42 pages, 8 figures