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arXiv · 0910.1958

On μ-Compatible Metrics and Measurable Sensitivity

Ilya Grigoriev·Nathaniel Ince·Marius Catalin Iordan·Amos Lubin·Cesar E. Silva
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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.

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Ilya Grigoriev, Nathaniel Ince, Marius Catalin Iordan, Amos Lubin, Cesar E. Silva. 2011-11-07. On μ-Compatible Metrics and Measurable Sensitivity. https://doi.org/10.4064/cm126-1-3

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