Minimal subdynamics and minimal flows without characteristic measures
Forum of Mathematics, Sigma, Tome 12 (2024)
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Given a countable group G and a G-flow X, a probability measure $\mu $ on X is called characteristic if it is $\mathrm {Aut}(X, G)$-invariant. Frisch and Tamuz asked about the existence of a minimal G-flow, for any group G, which does not admit a characteristic measure. We construct for every countable group G such a minimal flow. Along the way, we are motivated to consider a family of questions we refer to as minimal subdynamics: Given a countable group G and a collection of infinite subgroups $\{\Delta _i: i\in I\}$, when is there a faithful G-flow for which every $\Delta _i$ acts minimally?
@article{10_1017_fms_2024_41,
author = {Joshua Frisch and Brandon Seward and Andy Zucker},
title = {Minimal subdynamics and minimal flows without characteristic measures},
journal = {Forum of Mathematics, Sigma},
publisher = {mathdoc},
volume = {12},
year = {2024},
doi = {10.1017/fms.2024.41},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2024.41/}
}
TY - JOUR AU - Joshua Frisch AU - Brandon Seward AU - Andy Zucker TI - Minimal subdynamics and minimal flows without characteristic measures JO - Forum of Mathematics, Sigma PY - 2024 VL - 12 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.1017/fms.2024.41/ DO - 10.1017/fms.2024.41 LA - en ID - 10_1017_fms_2024_41 ER -
%0 Journal Article %A Joshua Frisch %A Brandon Seward %A Andy Zucker %T Minimal subdynamics and minimal flows without characteristic measures %J Forum of Mathematics, Sigma %D 2024 %V 12 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.1017/fms.2024.41/ %R 10.1017/fms.2024.41 %G en %F 10_1017_fms_2024_41
Joshua Frisch; Brandon Seward; Andy Zucker. Minimal subdynamics and minimal flows without characteristic measures. Forum of Mathematics, Sigma, Tome 12 (2024). doi: 10.1017/fms.2024.41
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