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.References
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Additional Information
- Hongbing Ju
- Affiliation: Department of Mathematics, Chinese University of Hong Kong, Shatin, Hong Kong
- Ka-Sing Lau
- Affiliation: Department of Mathematics, Chinese University of Hong Kong, Shatin, Hong Kong
- MR Author ID: 190087
- Email: kslau@math.cuhk.edu.hk
- Xiang-Yang Wang
- Affiliation: School of Mathematics and Computational Science, Sun Yat-Sen University, Guang-Zhou 510275, People’s Republic of China
- Email: mcswxy@mail.sysu.edu.cn
- Received by editor(s): October 12, 2009
- Received by editor(s) in revised form: December 4, 2009
- Published electronically: August 4, 2011
- Additional Notes: This research was partially supported by a HKRGC grant and a Direct Grant from CUHK
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 364 (2012), 103-118
- MSC (2010): Primary 28A78; Secondary 28A80
- DOI: https://doi.org/10.1090/S0002-9947-2011-05270-0
- MathSciNet review: 2833578