We study dynamical notions lying between $$\mathcal{U}$$
-frequent hypercyclicity and reiterative by investigating weighted upper densities the unweighted density Banach density. While chaos implies hypercyclicity, we show that does not imply with respect to any Moreover, if T is -frequently hypercyclic (resp. reiteratively hypercyclic) then n-fold product of still U-frequently this implicatio...