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Ergodicity and mixing via Young measures

Published online by Cambridge University Press:  06 August 2002

ZVI ARTSTEIN  and
MICHAEL GRINFELD
ZVI ARTSTEIN
Affiliation:
Department of Mathematics, The Weizmann Institute of Science, Rehovot 76100, Israel (e-mail: zvi.artstein@weizmann.ac.il)
MICHAEL GRINFELD
Affiliation:
Department of Mathematics, University of Strathclyde, Glasgow G1 1XH, UK (e-mail: michael@maths.strath.ac.uk)
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Abstract

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Connections are established between mixing or ergodic properties of maps on the one hand, and the convergence of the iterates of the map, or of the empirical measures of the iterates, to a constant measure-valued map, on the other. The uniqueness of an absolutely continuous ergodic measure can also be verified via the convergence. The technique helps to identify ergodic and mixing pairs and verify the uniqueness in specific examples.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 22 , Issue 4 , August 2002 , pp. 1001 - 1015
Copyright
© 2002 Cambridge University Press