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Recurrence in pairs

Published online by Cambridge University Press:  01 August 2008

KAMEL HADDAD  and
WILLIAM OTT
KAMEL HADDAD
Affiliation:
California State University, Bakersfield, Bakersfield, CA 93311, USA (email: [email protected])
WILLIAM OTT
Affiliation:
Courant Institute of Mathematical Sciences, New York, NY 10012, USA (email: [email protected])
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Abstract

We introduce and study the notion of weak product recurrence. Two sufficient conditions for this type of recurrence are established. We deduce that any point with a dense orbit in either the full one-sided shift on a finite number of symbols or a mixing subshift of finite type is weakly product recurrent. This observation implies that distality does not follow from weak product recurrence. We have therefore answered, in the negative, a question posed by Auslander and Furstenberg.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 28 , Issue 4 , August 2008 , pp. 1135 - 1143
Copyright
Copyright © 2008 Cambridge University Press

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References

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