Local Dimensions of Measures on Infinitely Generated Self-Affine Sets
Metric Geometry
2014-05-22 v2 Dynamical Systems
Abstract
We show the existence of the local dimension of an invariant probability measure on an infinitely generated self-affine set, for almost all translations. This implies that an ergodic probability measure is exactly dimensional. Furthermore the local dimension equals the minimum of the local Lyapunov dimension and the dimension of the space. We also give an estimate, that holds for all translation vectors, with only assuming the affine maps to be contractive.
Cite
@article{arxiv.1302.1435,
title = {Local Dimensions of Measures on Infinitely Generated Self-Affine Sets},
author = {Eino Rossi},
journal= {arXiv preprint arXiv:1302.1435},
year = {2014}
}
Comments
Accepted author manuscript, 10 pages