Asymptotic geometry of non-mixing sequences

Manfred Einsiedler, Tom Ward

Research output: Contribution to journalArticle

6 Citations (Scopus)

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 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.
Original languageEnglish
Pages (from-to)75-85
Number of pages11
JournalErgodic Theory and Dynamical Systems
Volume23
Issue number01
DOIs
Publication statusPublished - 2003

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