On $\mu $-compatible metrics and measurable sensitivity
Colloquium Mathematicum, Tome 126 (2012) no. 1, pp. 53-72
Cet article a éte moissonné depuis 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.
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
Affiliations des auteurs :
Ilya Grigoriev 1 ; Marius Cătălin Iordan 2 ; Amos Lubin 3 ; Nathaniel Ince 4 ; Cesar E. Silva 5
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author = {Ilya Grigoriev and Marius C\u{a}t\u{a}lin Iordan and Amos Lubin and Nathaniel Ince and Cesar E. Silva},
title = {On $\mu $-compatible metrics and measurable sensitivity},
journal = {Colloquium Mathematicum},
pages = {53--72},
year = {2012},
volume = {126},
number = {1},
doi = {10.4064/cm126-1-3},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm126-1-3/}
}
TY - JOUR AU - Ilya Grigoriev AU - Marius Cătălin Iordan AU - Amos Lubin AU - Nathaniel Ince AU - Cesar E. Silva TI - On $\mu $-compatible metrics and measurable sensitivity JO - Colloquium Mathematicum PY - 2012 SP - 53 EP - 72 VL - 126 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.4064/cm126-1-3/ DO - 10.4064/cm126-1-3 LA - en ID - 10_4064_cm126_1_3 ER -
%0 Journal Article %A Ilya Grigoriev %A Marius Cătălin Iordan %A Amos Lubin %A Nathaniel Ince %A Cesar E. Silva %T On $\mu $-compatible metrics and measurable sensitivity %J Colloquium Mathematicum %D 2012 %P 53-72 %V 126 %N 1 %U http://geodesic.mathdoc.fr/articles/10.4064/cm126-1-3/ %R 10.4064/cm126-1-3 %G en %F 10_4064_cm126_1_3
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
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