scholarly journals The Sierpiński gasket as the Martin boundary of a non-isotropic Markov chain

2020 ◽  
Vol 7 (2) ◽  
pp. 113-136
Author(s):  
Marc Kesseböhmer ◽  
Tony Samuel ◽  
Karenina Sender
Keyword(s):  
Markov Chain ◽  
Sierpinski Gasket ◽  
Martin Boundary ◽  
Sierpiński Gasket

Martin Metrics on the Sierpiński Gasket

2003 ◽  
Vol 03 (02) ◽  
pp. 267-277
Author(s):  
Atsushi Imai ◽  
Yasuhiro Kawasaki ◽  
Hiroshi Sato
Keyword(s):  
Dynamical System ◽  
Markov Chain ◽  
Topological Space ◽  
Sierpinski Gasket ◽  
Martin Boundary ◽  
Sierpiński Gasket ◽  
Hausdorff Dimensions ◽  
Lipschitz Equivalence ◽  
Euclidean Metric ◽  
Affine Mappings

It is known that the (N–1)-dimensional Sierpiński gasket [Formula: see text] is defined as an attractor of a dynamical system induced by affine mappings fi (i = 1, 2, …, N). Identifying fi with i, Denker and Sato [1] represented [Formula: see text] as the Martin boundary of a Markov chain on the word space generated by N letters. The Martin metrics determine a unique topological space on [Formula: see text] but are not always Lipschitz equivalent. In this paper, we characterize the Lipschitz equivalence of Martin metrics in terms of their coefficients, compare them with the Euclidean metric and compute their Hausdorff dimensions.

Martin boundary and exit space on the Sierpinski gasket

2011 ◽  
Vol 55 (3) ◽  
pp. 475-494 ◽  
Author(s):  
Ka-Sing Lau ◽  
Sze-Man Ngai
Keyword(s):  
Sierpinski Gasket ◽  
Martin Boundary ◽  
Sierpiński Gasket

scholarly journals Dimer Coverings on the Sierpinski Gasket

2008 ◽  
Vol 131 (4) ◽  
pp. 631-650 ◽  
Author(s):  
Shu-Chiuan Chang ◽  
Lung-Chi Chen
Keyword(s):  
Sierpinski Gasket ◽  
Sierpiński Gasket

scholarly journals Metric approximations of spectral triples on the Sierpiński gasket and other fractal curves

2021 ◽  
Vol 385 ◽  
pp. 107771
Author(s):  
Therese-Marie Landry ◽  
Michel L. Lapidus ◽  
Frédéric Latrémolière
Keyword(s):  
Sierpinski Gasket ◽  
Sierpiński Gasket ◽  
Spectral Triples

scholarly journals Level sets of harmonic functions on the Sierpiński gasket

2002 ◽  
Vol 40 (2) ◽  
pp. 335-362 ◽  
Author(s):  
Anders Öberg ◽  
Robert S. Strichartz ◽  
Andrew Q. Yingst
Keyword(s):  
Level Sets ◽  
Harmonic Functions ◽  
Sierpinski Gasket ◽  
Sierpiński Gasket

Design Sierpinski Gasket Antenna for WLAN Application

2007 ◽  
Author(s):  
C.Z.C. Ghani ◽  
M.H.A. Wahab ◽  
N. Abdullah ◽  
S.A Hamzah ◽  
A. Ubin ◽  
...  
Keyword(s):  
Sierpinski Gasket ◽  
Sierpiński Gasket

scholarly journals Gradients of Laplacian eigenfunctions on the Sierpinski gasket

2008 ◽  
Vol 137 (02) ◽  
pp. 531-540 ◽  
Author(s):  
Jessica L. DeGrado ◽  
Luke G. Rogers ◽  
Robert S. Strichartz
Keyword(s):  
Sierpinski Gasket ◽  
Sierpiński Gasket
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