When all points are generic for ergodic measures

• Autorzy: Downarowicz Tomasz , Weiss Benjamin

Identyfikatory

DOI

10.4064/ba210113-15-1

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

topological dynamical system; measure-preserving system; ergodic measure; semicontinuous partition; uniform system; strictly uniform system; semisimple system; generic point

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2020
• Tom: Vol. 68, no. 2
• Strony: 117--132
• Opis fizyczny: Bibliogr. 6 poz., rys.

Twórcy

autor

Downarowicz Tomasz

• Faculty of Pure and Applied Mathematics, Wrocław University of Technology, Wrocław, Poland

autor

Weiss Benjamin

• Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel

Bibliografia

• [H] G. Hansel, Strict uniformity in ergodic theory, Math. Z. 135 (1974), 221-248.
• [HY] J. G. Hocking and G. S. Young, Topology, Addison-Wesley, London, 1961.
• [J] R. I. Jewett, The prevalence of uniquely ergodic systems, J. Math. Mech. 19 (1970), 717-729.
• [KW] Y. Katznelson and B. Weiss, When all points are recurrent/generic, in: A. Katok (ed.), Ergodic Theory and Dynamical Systems I, Progr. Math. 10, Birkhäuser, Boston, MA, 1981, 195-210.
• [K] W. Krieger, On unique ergodicity, in: Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability, Vol. II, Univ. of California Press, 1972, 327-345.
• [O] J. C. Oxtoby, Ergodic sets, Bull. Amer. Math. Soc. 58 (1952), 116-136.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).