Measurable sensitivity
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- by Jennifer James, Thomas Koberda, Kathryn Lindsey, Cesar E. Silva and Peter Speh PDF
- Proc. Amer. Math. Soc. 136 (2008), 3549-3559 Request permission
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.References
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Additional Information
- 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
- MR Author ID: 842738
- ORCID: 0000-0001-5465-2651
- Email: koberda@math.harvard.edu
- Kathryn Lindsey
- Affiliation: Department of Mathematics, Cornell University, Ithaca, New York 14853-4201
- MR Author ID: 842785
- Email: klindsey@math.cornell.edu
- Cesar E. Silva
- Affiliation: Department of Mathematics, Williams College, Williamstown, Massachusetts 01267
- MR Author ID: 251612
- Email: csilva@williams.edu
- Peter Speh
- Affiliation: Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139-4307
- Email: pspeh@math.mit.edu
- Received by editor(s): December 8, 2006
- Received by editor(s) in revised form: July 25, 2007
- Published electronically: May 30, 2008
- Communicated by: Jane M. Hawkins
- © Copyright 2008 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 136 (2008), 3549-3559
- MSC (2000): Primary 37A05; Secondary 37F10
- DOI: https://doi.org/10.1090/S0002-9939-08-09294-0
- MathSciNet review: 2415039