Historic Behaviour for Random Expanding Maps on the Circle
Dynamical Systems
2017-10-30 v2
Abstract
Takens constructed a residual subset of the state space consisting of initial points with historic behaviour for expanding maps on the circle. We prove that this statistical property of expanding maps on the circle is preserved under small random perturbations. The proof is given by establishing a random Markov partition, which follows from a random version of Shub's Theorem on topological conjugacy with the folding maps.
Cite
@article{arxiv.1510.00905,
title = {Historic Behaviour for Random Expanding Maps on the Circle},
author = {Yushi Nakano},
journal= {arXiv preprint arXiv:1510.00905},
year = {2017}
}