\`x^2+y_1+z_12^34\`
Advanced Search
Article Contents
Article Contents

Rank as a function of measure

Abstract Related Papers Cited by
  • We establish certain topological properties of rank understood as a function on the set of invariant measures on a topological dynamical system. To be exact, we show that rank is of Young class LU (i.e., it is the limit of an increasing sequence of upper semicontinuous functions).
    Mathematics Subject Classification: Primary: 37A05; Secondary: 37A35.

    Citation:

    \begin{equation} \\ \end{equation}
  • [1]

    M. Boyle, D. Lind and D. Rudolph, The automorphism group of a shift of finite type, Trans. Amer. Math. Soc., 306 (1988), 71-114.doi: 10.1090/S0002-9947-1988-0927684-2.

    [2]

    N. Bourbaki, General Topology. Chapters 1-4, Translated from the French, reprint of the 1989 English translation, Elements of Mathematics (Berlin), Springer-Verlag, Berlin, 1998.

    [3]

    T. Downarowicz, Faces of simplexes of invariant measures, Israel J. Math., 165 (2008), 189-210.doi: 10.1007/s11856-008-1009-y.

    [4]

    T. Downarowicz, Entropy in dynamical systems, New Mathematical Monographs, 18, Cambridge University Press, Cambridge, 2011.doi: 10.1017/CBO9780511976155.

    [5]

    T. Downarowicz and J. Serafin, Possible entropy functions, Israel J. Math., 135 (2003), 221-250.doi: 10.1007/BF02776059.

    [6]

    S. Ferenczi, Systems of finite rank, Colloq. Math., 73 (1997), 35-65.

    [7]

    J. King, Joining-rank and the structure of finite rank mixing transformations, J. Analyse Math., 51 (1988), 182-227.doi: 10.1007/BF02791123.

    [8]

    I. Kornfeld and N. Ormes, Topological realizations of families of ergodic automorphisms, multitowers and orbit equivalence, Israel J. Math., 155 (2006), 335-357.doi: 10.1007/BF02773959.

    [9]

    D. S. Ornstein, D. J. Rudolph and B. Weiss, Equivalence of measure preserving transformations, Mem. Amer. Math. Soc., 37 (1982), xii+116 pp.doi: 10.1090/memo/0262.

    [10]

    H. L. Royden, Real Analysis, Third edition, Macmillan Publishing Company, New York, 1988.

    [11]

    W. H. Young, On a new method in the theory of integration, Proc. London Math. Soc., S2-9 (1911), 15-50.doi: 10.1112/plms/s2-9.1.15.

  • 加载中
SHARE

Article Metrics

HTML views() PDF downloads(144) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return