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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm126-1-3,
author = {Ilya Grigoriev and Marius C\u at\u alin Iordan and Amos Lubin and Nathaniel Ince and Cesar E. Silva},
title = {On $\mu$-compatible metrics and measurable sensitivity},
journal = {Colloquium Mathematicae},
volume = {126},
year = {2012},
pages = {53-72},
zbl = {1251.37011},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm126-1-3}
}
Ilya Grigoriev; Marius Cătălin Iordan; Amos Lubin; Nathaniel Ince; Cesar E. Silva. On μ-compatible metrics and measurable sensitivity. Colloquium Mathematicae, Tome 126 (2012) pp. 53-72. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm126-1-3/