Proceedings of the American Mathematical Society

Author(s): Jennifer James; Thomas Koberda; Kathryn Lindsey; Cesar E. Silva; Peter Speh
Journal: Proc. Amer. Math. Soc. 136 (2008), 3549-3559.
MSC (2000): Primary 37A05; Secondary 37F10
Posted: May 30, 2008
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Abstract: We introduce the notions of measurable and strong measurable sensitivity, which are measure-theoretic versions of the conditions of sensitive dependence on initial conditions and strong sensitive dependence on initial conditions, respectively. Strong measurable sensitivity is a consequence of light mixing, implies that a transformation has only finitely many eigenvalues, and does not exist in the infinite measure-preserving case. Unlike the traditional notions of sensitive dependence, measurable and strong measurable sensitivity carry up to measure-theoretic isomorphism, thus ignoring the behavior of the transformation on null sets and eliminating dependence on the choice of metric.

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Jennifer James
Affiliation: Department of Mathematics, Brandeis University, 415 South Street, Waltham, Massachusetts 02454
Email: jjames@brandeis.edu

Thomas Koberda
Affiliation: Department of Mathematics, Harvard University, 1 Oxford Street, Cambridge, Massachusetts 02138-2901
Email: koberda@math.harvard.edu

Kathryn Lindsey
Affiliation: Department of Mathematics, Cornell University, Ithaca, New York 14853-4201
Email: klindsey@math.cornell.edu

Cesar E. Silva
Affiliation: Department of Mathematics, Williams College, Williamstown, Massachusetts 01267
Email: csilva@williams.edu

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