Post-critically finite fractal and Martin boundary

DOI10.1090/S0002-9947-2011-05270-0zbMath1244.28004MaRDI QIDQ5388819

Hongbing Ju, Xiang-Yang Wang, Ka-Sing Lau

Publication date: 20 April 2012

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

Martin boundaryGreen functionharmonic functionsfractalstransition probabilitymonocyclicpost critically finite

Mathematics Subject Classification ID

Fractals (28A80) Hausdorff and packing measures (28A78)

Related Items

Boundary theory on the Hata tree ⋮ Denker–Sato type Markov chains and Harnack inequality ⋮ A note on measure-geometric Laplacians ⋮ A discrete Gauss-Green identity for unbounded Laplace operators, and the transience of random walks ⋮ Random walks and induced Dirichlet forms on self-similar sets ⋮ Martin boundary and exit space on the Sierpinski gasket ⋮ Self‐similar sets, simple augmented trees and their Lipschitz equivalence ⋮ On hyperbolic graphs induced by iterated function systems ⋮ Graphs induced by iterated function systems ⋮ Noncommutative Boundaries Arising in Dynamics and Representations of the Cuntz Relations ⋮ Gromov hyperbolic graphs arising from iterations ⋮ The Sierpiński gasket as the Martin boundary of a non-isotropic Markov chain ⋮ Denker-Sato type Markov chains on self-similar sets

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The difference between letters and a Martin kernel of a modulo 5 Markov chain
• The Laplacian on the Sierpinski gasket via the method of averages.
• Markoff chains and Martin boundaries
• Sierpiński gasket as a Martin boundary. II: The intrinsic metric
• Self-similar sets as hyperbolic boundaries
• Dirichlet forms on quotients of shift spaces
• Open set condition and post-critically finite self-similar sets
• Harmonic Calculus on P.C.F. Self-Similar Sets
• Fractafolds based on the Sierpinski gasket and their spectra
• Reflections on Harmonic Analysis of the Sierpiński Gasket
• Random Walks on Infinite Graphs and Groups
• Topology and separation of self-similar fractals in the plane
• BOUNDARY THEORY OF MARKOV PROCESSES (THE DISCRETE CASE)
• Minimal Positive Harmonic Functions
• Lectures on Choquet's theorem
• Sierpiński gasket as a Martin boundary. I: Martin kernels