Sensitivity and historic behavior for continuous maps on Baire metric spaces
Dynamical Systems
2021-11-16 v1
Abstract
We introduce a notion of sensitivity, with respect to a continuous bounded observable, which provides a sufficient condition for a continuous map, acting on a Baire metric space, to exhibit a Baire generic subset of points with historic behavior. The applications of this criterion recover, and extend, several known theorems on the genericity of the irregular set, besides yielding a number of new results, including information on the irregular set of geodesic flows, in both negative and non-positive curvature, and semigroup actions.
Cite
@article{arxiv.2111.07215,
title = {Sensitivity and historic behavior for continuous maps on Baire metric spaces},
author = {M. Carvalho and V. Coelho and L. Salgado and P. Varandas},
journal= {arXiv preprint arXiv:2111.07215},
year = {2021}
}