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Ledrappier’s system is almost mixing of all orders

Published online by Cambridge University Press:  01 April 2008

L. ARENAS-CARMONA ,
D. BEREND  and
V. BERGELSON
L. ARENAS-CARMONA
Affiliation:
Department of Mathematics, University of Chile, Casilla 653, Santiago, Chile (email: [email protected])
D. BEREND
Affiliation:
Departments of Mathematics and Computer Science, Ben-Gurion University, Beer Sheva 84105, Israel (email: [email protected])
V. BERGELSON
Affiliation:
Department of Mathematics, Ohio State University, Columbus, OH 43210, USA (email: [email protected])
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Abstract

We consider Ledrappier’s dynamical system, which was the first example of a -action which is 2-mixing but not 3-mixing. Our main result is that, excluding certain small ‘constructible’ sets, the system is mixing of every order.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 28 , Issue 2: William Parry Memorial Volume , April 2008 , pp. 339 - 365
Copyright
Copyright © Cambridge University Press 2008

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