Oscillating statistics of transitive dynamics
Dynamical Systems
2016-06-28 v2
Abstract
We prove that topologically generic orbits of C0 transitive and non-uniquely ergodic dynamical systems, exhibit an extremely oscillating asymptotical statistics. Precisely, the minimum weak* compact set of invariant probabilities, that describes the asymptotical statistics of each orbit of a residual set, contains all the ergodic probabilities. If besides f is ergodic with respect to the Lebesgue measure, then also Lebesgue-almost all the orbits exhibit that kind of extremely oscillating statistics.
Cite
@article{arxiv.1502.04400,
title = {Oscillating statistics of transitive dynamics},
author = {Eleonora Catsigeras},
journal= {arXiv preprint arXiv:1502.04400},
year = {2016}
}
Comments
This revised version has some new paragraphs at the introduction according to the suggestion of the referee