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When all points are generic for ergodic measures

Tom 68 / 2020

Tomasz Downarowicz, Benjamin Weiss Bulletin Polish Acad. Sci. Math. 68 (2020), 117-132 MSC: Primary 37B05, 37B20; Secondary 37A25. DOI: 10.4064/ba210113-15-1 Opublikowany online: 25 January 2021

Streszczenie

We establish connections between several properties of topological dynamical systems, such as:

– every point is generic for an ergodic measure,

– the map sending points to the measures they generate is continuous,

– the system splits into uniquely (alternatively, strictly) ergodic subsystems,

– the map sending ergodic measures to their topological supports is continuous,

– the Cesàro means of every continuous function converge uniformly.

Autorzy

  • Tomasz DownarowiczFaculty of Pure and Applied Mathematics
    Wrocław University of Technology
    Wrocław, Poland
    e-mail
  • Benjamin WeissEinstein Institute of Mathematics
    The Hebrew University of Jerusalem
    Jerusalem, Israel
    e-mail

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