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Asymptotic geometry of non-mixing sequences

Einsiedler, M.; Ward, T.

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Authors

M. Einsiedler

T. Ward



Abstract

The exact order of mixing for zero-dimensional algebraic dynamical systems is not entirely understood. Here we use valuations in function fields to exhibit an asymptotic shape in non-mixing sequences for algebraic Z^2-actions. This gives a relationship between the order of mixing and the convex hull of the defining polynomial. Using this result, we show that an algebraic dynamical system for which any shape of cardinality three is mixing is mixing of order three, and for any k greater than or equal to 1 exhibit examples that are k-fold mixing but not (k+1)-fold mixing.

Citation

Einsiedler, M., & Ward, T. (2003). Asymptotic geometry of non-mixing sequences. Ergodic Theory and Dynamical Systems, 23(1), 75-85. https://doi.org/10.1017/s0143385702000950

Journal Article Type Article
Publication Date Feb 1, 2003
Deposit Date Oct 12, 2012
Publicly Available Date Oct 24, 2012
Journal Ergodic Theory and Dynamical Systems
Print ISSN 0143-3857
Electronic ISSN 1469-4417
Publisher Cambridge University Press
Peer Reviewed Peer Reviewed
Volume 23
Issue 1
Pages 75-85
DOI https://doi.org/10.1017/s0143385702000950

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