Dirichlet forms on unconstrained Sierpinski carpets

2021/04/04 by Shiping Cao, Cao, Shiping, Hua Qiu +1 · 2 citations
Mathematics · Physics and Astronomy · #28A80 #31E05 #FOS: Mathematics #Functional Analysis (math.FA) #History and Theory of Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2104.01529

openalex publication_date 2021/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct symmetric self-similar Dirichlet forms on unconstrained Sierpinski carpets, which are natural extension of planar Sierpinski carpets by allowing the small cells to live off the 1/k grids. The intersection of two cells can be a line segment of irrational length, and the non-diagonal assumption is dropped in this recurrent setting.

Citations

• Brownian Motion and Harmonic Analysis on Sierpinski Carpets
• Transition density estimates for Brownian motion on affine nested fractals
• Brownian motion on nested fractals
• Existence and uniqueness of diffusions on the Julia sets of Misiurewicz-Sierpinski maps

Cited by

• A non-canonical diffusion on the Sierpiński carpet
• BGD domains in p.c.f. self-similar sets II: spectral asymptotics for Laplacians

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• Local and Non-Local Dirichlet Forms on the Sierpiński Gasket and the Sierpiński Carpet