Geodesic
On $\mu $-compatible metrics and measurable sensitivity
Ilya Grigoriev1 ; Marius Cătălin Iordan2 ; Amos Lubin3 ; Nathaniel Ince4 ; Cesar E. Silva5
1 Department of Mathematics Stanford University Stanford, CA 94305, U.S.A.
2 Williams College Williamstown, MA 01267, U.S.A.
3 Harvard College University Hall Cambridge, MA 02138, U.S.A.
4 Massachusetts Institute of Technology 77 Massachusetts Ave. Cambridge, MA 02139-4307, U.S.A.
5 Department of Mathematics Williams College Williamstown, MA 01267, U.S.A.
Colloquium Mathematicum, Tome 126 (2012) no. 1, pp. 53-72.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/cm126-1-3
Keywords: introduce notion w measurable sensitivity which extends strictly implies canonical measurable sensitivity measure theoretic version sensitive dependence initial conditions notion implies pairwise sensitivity respect large class metrics nonsingular ergodic conservative dynamical systems standard spaces either w measurably sensitive isomorphic mod nbsp minimal uniformly rigid isometry finite measure preserving w measurably sensitive measurably isomorphic ergodic isometry compact metric space

Ilya Grigoriev 1 ; Marius Cătălin Iordan 2 ; Amos Lubin 3 ; Nathaniel Ince 4 ; Cesar E. Silva 5

1 Department of Mathematics Stanford University Stanford, CA 94305, U.S.A.
2 Williams College Williamstown, MA 01267, U.S.A.
3 Harvard College University Hall Cambridge, MA 02138, U.S.A.
4 Massachusetts Institute of Technology 77 Massachusetts Ave. Cambridge, MA 02139-4307, U.S.A.
5 Department of Mathematics Williams College Williamstown, MA 01267, U.S.A. 
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Ilya Grigoriev; Marius Cătălin Iordan; Amos Lubin; Nathaniel Ince; Cesar E. Silva. On $\mu $-compatible metrics and measurable sensitivity. Colloquium Mathematicum, Tome 126 (2012) no. 1, pp. 53-72. doi : 10.4064/cm126-1-3. http://geodesic.mathdoc.fr/articles/10.4064/cm126-1-3/

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