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We show that the dynamic asymptotic dimension of a minimal free action of aninfinite virtually cyclic group on a compact Hausdorff space is always one.This extends a well-known result of Guentner, Willett, and Yu for minimal freeactions of infinite cyclic groups. Furthermore, the minimality assumption canbe replaced by the marker property, and we prove the marker property for allfree actions of countable groups on finite dimensional compact Hausdorffspaces, generalising a result of Szabo in the metrisable setting.

Dynamic asymptotic dimension for actions of virtually cyclic groups