Invariant measures for typical continuous maps on manifolds
Dynamical Systems
2020-01-08 v1
Abstract
We study the invariant measures of typical maps on compact connected manifolds with or without boundary, and also of typical homeomorphisms. We prove that the weak closure of the set of ergodic measurescoincides with the weak closure of the set of measures supported on periodic orbits and also coincides withthe set of pseudo-physical measures. Furthermore, we show that this set has empty interior in the set of invariant measures.
Cite
@article{arxiv.1811.04805,
title = {Invariant measures for typical continuous maps on manifolds},
author = {Eleonora Catsigeras and Serge Troubetzkoy},
journal= {arXiv preprint arXiv:1811.04805},
year = {2020}
}
Comments
arXiv admin note: text overlap with arXiv:1705.10133