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On μ-compatible metrics and measurable sensitivity

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Grigoriev I., Iordan M., Lubin A., Ince N., Silva C.

Colloquium Mathematicum

2012

tom 126

nr 1

53-72

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.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Grigoriev I.

1 Ince N.

1 Iordan M.

1 Lubin A.

1 Silva C.

1 2012

Wyniki wyszukiwania

On μ-compatible metrics and measurable sensitivity