Asymptotic geometry of non-mixing sequences

Einsiedler, Manfred and Ward, Tom (2003) Asymptotic geometry of non-mixing sequences. Ergodic Theory and Dynamical Systems, 23 (01). pp. 75-85. ISSN 0143-3857

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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 Z2-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.

Item Type: Article
Faculty \ School: Faculty of Science > School of Mathematics
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Depositing User: Vishal Gautam
Date Deposited: 18 Mar 2011 14:48
Last Modified: 07 Mar 2023 17:30
DOI: 10.1017/S0143385702000950

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