Pseudo-physical measures for typical continuous maps of the interval
Dynamical Systems
2017-05-30 v1
Abstract
We study the measure theoretic properties of typical C 0 maps of the interval. We prove that any ergodic measure is pseudo-physical, and conversely, any pseudo-physical measure is in the closure of the ergodic measures, as well as in the closure of the atomic measures. We show that the set of pseudo-physical measures is meager in the space of all invariant measures. Finally, we study the entropy function. We construct pseudo-physical measures with infinite entropy. We also prove that, for each m 1, there exists infinitely many pseudo-physical measures with entropy log m, and deduce that the entropy function is neither upper semi-continuous nor lower semi-continuous.
Cite
@article{arxiv.1705.10133,
title = {Pseudo-physical measures for typical continuous maps of the interval},
author = {Eleonora Catsigeras and Serge Troubetzkoy},
journal= {arXiv preprint arXiv:1705.10133},
year = {2017}
}