  In mixed systems, besides regular and chaotic states, there are states
supported by the chaotic region mainly living in the vicinity of the hierarchy
of regular islands. We show that the fraction of these hierarchical states
scales as $\hbar^{-\alpha}$ and relate the exponent $\alpha=1-1/\gamma$ to the
decay of the classical staying probability $P(t)\sim t^{-\gamma}$. This is
numerically confirmed for the kicked rotor by studying the influence of
hierarchical states on eigenfunction and level statistics.
