Open AccessAsymptotic geometry of non-mixing sequences
Author(s) -
Manfred Einsiedler,
Thomas Ward
Publication year - 2003
Publication title -
ergodic theory and dynamical systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.571
H-Index - 61
eISSN - 1469-4417
pISSN - 0143-3857
DOI - 10.1017/s0143385702000950
Subject(s) - mixing (physics) , mathematics , algebraic number , polynomial , cardinality (data modeling) , order (exchange) , dynamical systems theory , pure mathematics , combinatorics , mathematical analysis , geometry , physics , computer science , quantum mechanics , finance , economics , data mining
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
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