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Measurable Sensitivity

Jennifer James·Thomas Koberda·Kathryn Lindsey·Cesar E. Silva·Peter Speh
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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.

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BibTeXRIS

Jennifer James, Thomas Koberda, Kathryn Lindsey, Cesar E. Silva, Peter Speh. 2006-12-19. Measurable Sensitivity. https://arxiv.org/abs/math/0612480

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