"Characterizations of rank-one transformations that factor onto an odometer, or are isomorphic to an odometer

Abstract: We will start by discussing rank-one transformations and odometer transformations, and review the isomorphism problem in ergodic theory. We will then present explicit characterizations, based on the cutting and spacer parameters of the rank-one transformation, of (a) which rank-one transformations factor onto a given finite cyclic permutation, (b) which rank-one transformations factor onto a given odometer, and (c) which rank-one transformations are isomorphic to a given odometer. These naturally yield characterizations of (d) which rank-one transformations factor onto some (unspecified) finite cyclic permutation, (e) which rank-one transformations factor onto some (unspecified) odometer, and (f) which rank-one transformations are isomorphic to some (unspecified) odometer. This is joint work with Matthew Foreman, Su Gao, Aaron Hill, and Benjamin Weiss.

dynamical systems

Audience: researchers in the topic

Little school dynamics

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