Minimal distance between random orbits
Dynamical Systems
2022-09-28 v1
Abstract
We study the minimal distance between two orbit segments of length n, in a random dynamical system with sufficiently good mixing properties. This problem has already been solved in non-random dynamical system, and on average in random dynamical systems (the so-called annealed version of the problem): it is known that the asymptotic behavior for this question is given by a dimension-like quantity associated to the invariant measure, called its correlation dimension (or R{\'e}nyi entropy). We study the analogous quenched question, and show that the asymptotic behavior is more involved: two correlation dimensions show up, giving rise to a non-smooth behavior of the associated asymptotic exponent.
Keywords
Cite
@article{arxiv.2209.13240,
title = {Minimal distance between random orbits},
author = {Sébastien Gouëzel and Jérôme Rousseau and Manuel Stadlbauer},
journal= {arXiv preprint arXiv:2209.13240},
year = {2022}
}