Measurable Sensitivity
Dynamical Systems
2011-05-10 v2
Abstract
We introduce the notion of measurable sensitivity, a measure-theoretic version of the condition of sensitive dependence on initial conditions. It is a consequence of light mixing, implies a transformation has only finitely many eigenvalues, and does not exist in the infinite measure-preserving case. Unlike the traditional notion of sensitive dependence, measurable sensitivity carries up to measure-theoretic isomorphism, thus ignoring the behavior of the function on null sets and eliminating dependence on the choice of metric.
Cite
@article{arxiv.math/0612480,
title = {Measurable Sensitivity},
author = {Jennifer James and Thomas Koberda and Kathryn Lindsey and Cesar E. Silva and Peter Speh},
journal= {arXiv preprint arXiv:math/0612480},
year = {2011}
}