Neutralized local entropy, and dimension bounds for invariant measurs
Dynamical Systems
2023-07-31 v2
Abstract
We introduce a notion of a point-wise entropy of measures (i.e local entropy) called neutralized local entropy, and compare it with the Brin-Katok local entropy. We show that the neutralized local entropy coincides with Brin-Katok local entropy almost everywhere. Neutralized local entropy is computed by measuring open sets with a relatively simple geometric description. Our proof uses a measure density lemma for Bowen balls, and a version of a Besicovitch covering lemma for Bowen balls. As an application, we prove a lower point-wise dimension bound for invariant measures, complementing the previously established bounds for upper point-wise dimension.
Keywords
Cite
@article{arxiv.2302.10874,
title = {Neutralized local entropy, and dimension bounds for invariant measurs},
author = {Snir Ben Ovadia and Federico Rodriguez-Hertz},
journal= {arXiv preprint arXiv:2302.10874},
year = {2023}
}