Post-critically finite fractal and Martin boundary

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

doi:10.1090/S0002-9947-2011-05270-0

Post-critically finite fractal and Martin boundary
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by Hongbing Ju, Ka-Sing Lau and Xiang-Yang Wang PDF

Trans. Amer. Math. Soc. 364 (2012), 103-118 Request permission

Abstract:

For an iterated function system (IFS), which we call simple post critically finite, we introduce a Markov chain on the corresponding symbolic space and study its boundary behavior. We carry out some fine estimates of the Martin metric and use them to prove that the Martin boundary can be identified with the invariant set (fractal) of the IFS. This enables us to bring in the boundary theory of Markov chains and the discrete potential theory on this class of fractal sets.

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