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Given a countable group $G$ and a $G$-flow $X$, a measure $\mu\in P(X)$ iscalled characteristic if it is $\mathrm{Aut}(X, G)$-invariant. Frisch and Tamuzasked about the existence of a minimal $G$-flow, for any group $G$, which doesnot 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 ofquestions we refer to as minimal subdynamics: Given a countable group $G$ and acollection of infinite subgroups $\{\Delta_i: i\in I\}$, when is there afaithful $G$-flow for which every $\Delta_i$ acts minimally?

Minimal subdynamics and minimal flows without characteristic measures