Measurable sensitivity
Authors:
Jennifer James, Thomas Koberda, Kathryn Lindsey, Cesar E. Silva and Peter Speh
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
Published electronically:
May 30, 2008
MathSciNet review:
2415039
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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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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
Keywords:
Measure-preserving,
ergodic,
sensitive dependence
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
Article copyright:
© Copyright 2008
American Mathematical Society
