  Blenders are special hyperbolic sets used to produce various robust dynamical
phenomena which appear fragile at first glance. We prove for $C^r$
diffeomorphisms ($r=2,\dots,\infty,\omega$) that blenders naturally exist
(without perturbation) near non-degenerate heterodimensional cycles of
coindex-1, and the existence is determined by arithmetic properties of moduli
of topological conjugacy for diffeomorphisms with heterodimensional cycles. In
particular, we obtain a $C^r$-generic dichotomy for dynamics in any small
neighborhood $U$ of a non-degenerate heterodimensional cycle: either there
exist infinitely many blenders accumulating on the cycle, forming robust
heterodimensional dynamics in most cases, or there are no orbits other than
those constituting the cycle lying entirely in $U$.
