Measurable Sensitivity

Details Measurable Sensitivity Measurable Sensitivity

2006-12-17

arxiv.org/abs/math/0612480v2

Proc. Amer. Math. Soc. 136 (2008), no. 10, 3549--3559

Mathematics

Dynamical Systems

Scientific paper

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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