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On invariant distributions and mixing

Published online by Cambridge University Press:  28 November 2006

YVES COUDENE
YVES COUDENE
Affiliation:
IRMAR, Université Rennes 1, campus beaulieu, bâtiment 23, 35042 Rennes cedex, France (e-mail: yves.coudene@univ-rennes1.fr)
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Abstract

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We show that any probability preserving transformation of a metric space is mixing as soon as there are no non-constant $L^2$-functions which are invariant under both the stable and unstable distributions. This generalizes a result of Babillot.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 27 , Issue 1 , February 2007 , pp. 109 - 112
Copyright
2006 Cambridge University Press