On μ-compatible metrics and measurable sensitivity

Ilya Grigoriev, et al. "On μ-compatible metrics and measurable sensitivity." Colloquium Mathematicae 126.1 (2012): 53-72. <http://eudml.org/doc/286534>.

@article{IlyaGrigoriev2012,
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.},
author = {Ilya Grigoriev, Marius Cătălin Iordan, Amos Lubin, Nathaniel Ince, Cesar E. Silva},
journal = {Colloquium Mathematicae},
keywords = {measure-preserving transformation; nonsingular transformation; ergodic; sensitive dependence; -compatible metrics},
language = {eng},
number = {1},
pages = {53-72},
title = {On μ-compatible metrics and measurable sensitivity},
url = {http://eudml.org/doc/286534},
volume = {126},
year = {2012},
}

TY - JOUR
AU - Ilya Grigoriev
AU - Marius Cătălin Iordan
AU - Amos Lubin
AU - Nathaniel Ince
AU - Cesar E. Silva
TI - On μ-compatible metrics and measurable sensitivity
JO - Colloquium Mathematicae
PY - 2012
VL - 126
IS - 1
SP - 53
EP - 72
AB - 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.
LA - eng
KW - measure-preserving transformation; nonsingular transformation; ergodic; sensitive dependence; -compatible metrics
UR - http://eudml.org/doc/286534
ER -