Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 37A05, 37F10

Retrieve articles in all journals with MSC (2000): 37A05, 37F10


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
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

Peter Speh
Affiliation: Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139-4307
Email: pspeh@math.mit.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09294-0
PII: S 0002-9939(08)09294-0
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