There are no $\sigma$-finite absolutely continuous invariant measures for multicritical circle maps
Dynamical Systems
2021-10-04 v1
Abstract
It is well-known that every multicritical circle map without periodic orbits admits a unique invariant Borel probability measure which is purely singular with respect to Lebesgue measure. Can such a map leave invariant an infinite, -finite invariant measure which is absolutely continuous with respect to Lebesgue measure? In this paper, using an old criterion due to Katznelson, we show that the answer to this question is no.
Keywords
Cite
@article{arxiv.2007.10444,
title = {There are no $\sigma$-finite absolutely continuous invariant measures for multicritical circle maps},
author = {Edson de Faria and Pablo Guarino},
journal= {arXiv preprint arXiv:2007.10444},
year = {2021}
}
Comments
23 pages, 2 figures