Abstract
F. 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.
Citation
Yushi NAKANO. "Historic Behaviour for Random Expanding Maps on the Circle." Tokyo J. Math. 40 (1) 165 - 184, June 2017. https://doi.org/10.3836/tjm/1502179221
Information