On the closedness of ergodic measures in a characteristic class

Fuente: arXiv
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Autori principali: Babel, Sejal, Łącka, Martha
Natura: Preprint
Pubblicazione: 2025
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author Babel, Sejal
Łącka, Martha
author_facet Babel, Sejal
Łącka, Martha
contents We endow the set of all invariant measures of a topological dynamical system with a metric $\barρ$, which induces a topology stronger than the the weak$^*$-topology. Then, we study the closedness of ergodic measures within a characteristic class under this metric. Specifically, we show that if a sequence of generic points associated with ergodic measures from a fixed characteristic class converges in the Besicovitch pseudometric, then the limit point is generic for an ergodic measure in the same class. This implies that the set of ergodic measures belonging to a fixed characteristic class is closed in $\barρ$ (by a result of Babel, Can, Kwietniak, and Oprocha in [1]).
format Preprint
id arxiv_https___arxiv_org_abs_2510_26564
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle On the closedness of ergodic measures in a characteristic class
Babel, Sejal
Łącka, Martha
Dynamical Systems
37A05
We endow the set of all invariant measures of a topological dynamical system with a metric $\barρ$, which induces a topology stronger than the the weak$^*$-topology. Then, we study the closedness of ergodic measures within a characteristic class under this metric. Specifically, we show that if a sequence of generic points associated with ergodic measures from a fixed characteristic class converges in the Besicovitch pseudometric, then the limit point is generic for an ergodic measure in the same class. This implies that the set of ergodic measures belonging to a fixed characteristic class is closed in $\barρ$ (by a result of Babel, Can, Kwietniak, and Oprocha in [1]).
title On the closedness of ergodic measures in a characteristic class
topic Dynamical Systems
37A05
url https://arxiv.org/abs/2510.26564