Self-similar Dirichlet forms on polygon carpets

2022/05/27 by Shiping Cao, Cao, Shiping, Hua Qiu +3 · 1 citation
Mathematics · #28A80 #31E05 #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2206.00040

openalex publication_date 2022/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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• A non-canonical diffusion on the Sierpiński carpet

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