On natural invariant measures on generalised iterated function systems
Dynamical Systems
2017-01-31 v1
Abstract
We consider the limit set of generalised iterated function systems. Under the assumption of a natural potential, the so called cylinder function, we prove the existence of the invariant probability measure satisfying the equilibrium state. We motivate this approach by showing that for typical self-affine sets there exists an ergodic invariant measure having the same Hausdorff dimension as the set itself.
Cite
@article{arxiv.1701.08575,
title = {On natural invariant measures on generalised iterated function systems},
author = {Antti Käenmäki},
journal= {arXiv preprint arXiv:1701.08575},
year = {2017}
}