On μ-compatible metrics and measurable sensitivity

• Autorzy: Ilya Grigoriev , Marius Cătălin Iordan , Amos Lubin , Nathaniel Ince , Cesar E. Silva
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 37A05: Measure-preserving transformations
• 37A40: Nonsingular (and infinite-measure preserving) transformations
• 37F10: Polynomials; rational maps; entire and meromorphic functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2012
• Tom: 126
• Numer: 1
• Strony: 53-72

Daty

wydano

2012

Twórcy

autor

Ilya Grigoriev

• Department of Mathematics, Stanford University, Stanford, CA 94305, U.S.A.

autor

Marius Cătălin Iordan

• Williams College, Williamstown, MA 01267, U.S.A.

autor

Amos Lubin

• Harvard College, University Hall, Cambridge, MA 02138, U.S.A.

autor

Nathaniel Ince

• Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, MA 02139-4307, U.S.A.

autor

Cesar E. Silva

• Department of Mathematics, Williams College, Williamstown, MA 01267, U.S.A.

Identyfikatory

DOI

10.4064/cm126-1-3