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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    DANILENKO, ALEXANDRE I. 2014. Mixing actions of the Heisenberg group. Ergodic Theory and Dynamical Systems, Vol. 34, Issue. 04, p. 1142.

    Aiello, Domenico Diao, Hansheng Fan, Zhou King, Daniel O Lin, Jessica and Silva, Cesar E 2012. Measurable time-restricted sensitivity. Nonlinearity, Vol. 25, Issue. 12, p. 3313.

    EL ABDALAOUI, EL HOUCEIN 2007. A new class of rank-one transformations with singular spectrum. Ergodic Theory and Dynamical Systems, Vol. 27, Issue. 05,

    Рыжиков, Валерий Валентинович and Ryzhikov, Valerii Valentinovich 2007. Слабые пределы степеней, простой спектр симметрических произведений и перемешивающие конструкции ранга 1. Математический сборник, Vol. 198, Issue. 5, p. 137.

    Danilenko, Alexandre I. 2006. Mixing rank-one actions for infinite sums of finite groups. Israel Journal of Mathematics, Vol. 156, Issue. 1, p. 341.

    Ryzhikov, V. V. 2006. On the spectral and mixing properties of rank-one constructions in ergodic theory. Doklady Mathematics, Vol. 74, Issue. 1, p. 545.


Mixing on a class of rank-one transformations

  • DARREN CREUTZ (a1) and CESAR E. SILVA (a1)
  • DOI:
  • Published online: 01 March 2004

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 a family of what we call dynamical sequences. The application of our theorem shows that the class of polynomial rank-one transformations, rank-one transformations where the spacers are chosen to be the values of a polynomial with some mild conditions on the polynomials, that have restricted growth are mixing transformations, implying, in particular, Adams' result on staircase transformations. Another application yields a new proof that Ornstein's class of rank-one transformations constructed using ‘random spacers’ are almost surely mixing transformations.

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Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
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