On \mu-Compatible Metrics and Measurable Sensitivity
Dynamical Systems
2012-08-20 v2
Abstract
We introduce the notion of W-measurable sensitivity, which extends and strictly implies canonical measurable sensitivity, a measure- theoretic version of sensitive dependence on initial conditions. This notion also implies pairwise sensitivity with respect to a large class of metrics. We show that nonsingular ergodic and conservative dynamical systems on standard spaces must be either W-measurably sensitive, or isomorphic mod 0 to a minimal uniformly rigid isometry. In the finite measure-preserving case they are W-measurably sensitive or measurably isomorphic to an ergodic isometry on a compact metric space.
Cite
@article{arxiv.0910.1958,
title = {On \mu-Compatible Metrics and Measurable Sensitivity},
author = {Ilya Grigoriev and Nathaniel Ince and Marius Catalin Iordan and Amos Lubin and Cesar E. Silva},
journal= {arXiv preprint arXiv:0910.1958},
year = {2012}
}
Comments
Many improvements in exposition, a technical assumption removed, as suggested by the reviewer