Creutz, Darren; Silva, Cesar E. Mixing on a class of rank-one transformations. (English) Zbl 1066.37003 Ergodic Theory Dyn. Syst. 24, No. 2, 407-440 (2004). Authors’ abstract: 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. Reviewer: Idris Assani (Chapel Hill) Cited in 1 ReviewCited in 12 Documents MSC: 37A25 Ergodicity, mixing, rates of mixing 37A05 Dynamical aspects of measure-preserving transformations 28D05 Measure-preserving transformations Keywords:mixing; rank-one transformations; uniform ergodicity PDFBibTeX XMLCite \textit{D. Creutz} and \textit{C. E. Silva}, Ergodic Theory Dyn. Syst. 24, No. 2, 407--440 (2004; Zbl 1066.37003) Full Text: DOI arXiv