Mixing on a class of rank one transformations

Details Mixing on a class of rank one transformations Mixing on a class of rank one transformations

2001-09-21

arxiv.org/abs/math/0109159v1

Mathematics

Dynamical Systems

27 pages

Scientific paper

We prove that a rank one transformation satisfying a condition called restricted growth is a mixing transformation if and only if the spacer sequence for the transformation is uniformly ergodic. Uniform ergodicity is a generalization of the notion of ergodicity for sequences in the sense that the mean ergodic theorem holds for what we call dynamical sequences. In particular, Adams' class of staircase transformations and Ornstein's class constructed using ``random spacers'' have both restricted growth and uniformly ergodic spacer sequences.

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