Geodesic
When all points are generic for ergodic measures
Tomasz Downarowicz1 ; Benjamin Weiss2
1Faculty of Pure and Applied Mathematics Wrocław University of Technology Wrocław, Poland
2Einstein Institute of Mathematics The Hebrew University of Jerusalem Jerusalem, Israel
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 68 (2020) no. 2, pp. 117-132
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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.
DOI : 10.4064/ba210113-15-1
Keywords: establish connections between several properties topological dynamical systems every point generic ergodic measure map sending points measures generate continuous system splits uniquely alternatively strictly ergodic subsystems map sending ergodic measures their topological supports continuous ces means every continuous function converge uniformly

Tomasz Downarowicz  1   ; Benjamin Weiss  2

1 Faculty of Pure and Applied Mathematics Wrocław University of Technology Wrocław, Poland
2 Einstein Institute of Mathematics The Hebrew University of Jerusalem Jerusalem, Israel 
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Tomasz Downarowicz; Benjamin Weiss. When all points are generic for ergodic measures. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 68 (2020) no. 2, pp. 117-132. doi: 10.4064/ba210113-15-1

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