Post-critically finite fractal and martin boundary
Publication in refereed journal


Times Cited
Altmetrics Information
.

Other information
AbstractFor 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. © 2011 American Mathematical Societ.
All Author(s) ListJu H., Lau K.-S., Wang X.-Y.
Journal nameTransactions of the American Mathematical Society
Year2012
Month1
Day1
Volume Number364
Issue Number1
PublisherAmerican Mathematical Society
Place of PublicationUnited States
Pages103 - 118
ISSN0002-9947
eISSN1088-6850
LanguagesEnglish-United Kingdom
KeywordsFractals, Green function, Harmonic functions, Martin boundary, Monocyclic, Post critically finite, Transition probability

Last updated on 2021-16-01 at 00:36