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Displaying similar documents to “Finite rank d actions and the loosely Bernoulli property.”

Phenomena in rank-one ℤ²-actions

Tomasz Downarowicz, Jacek Serafin (2009)

Studia Mathematica

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We present an example of a rank-one partially mixing ℤ²-action which possesses a non-rigid factor and for which the Weak Closure Theorem fails. This is in sharp contrast to one-dimensional actions, which cannot display this type of behavior.

Mixing on rank-one transformations

Darren Creutz, Cesar E. Silva (2010)

Studia Mathematica

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We prove that mixing on rank-one transformations is equivalent to "the uniform convergence of ergodic averages (as in the mean ergodic theorem) over subsequences of partial sums". In particular, all polynomial staircase transformations are mixing.