Geometry of measures in random systems with complete connections
Dynamical Systems
2022-02-16 v1 Probability
Abstract
We study new relations between countable iterated function systems (IFS) with overlaps, Smale endomorphisms and random systems with complete connections. We prove that stationary measures for countable conformal IFS with overlaps and placedependent probabilities, are exact dimensional; moreover we determine their Hausdorff dimension. Next, we construct a family of fractals in the limit set of a countable IFS with overlaps S, and study the dimension for certain measures supported on these subfractals. In particular, we obtain families of measures on these subfractals which are related to the geometry of the system.
Keywords
Cite
@article{arxiv.2202.07335,
title = {Geometry of measures in random systems with complete connections},
author = {Eugen Mihailescu and Mariusz Urbanski},
journal= {arXiv preprint arXiv:2202.07335},
year = {2022}
}