  We discuss the coarse-grained level density of the H\'enon-Heiles system
above the barrier energy, where the system is nearly chaotic. We use periodic
orbit theory to approximate its oscillating part semiclassically via
Gutzwiller's semiclassical trace formula (extended by uniform approximations
for the contributions of bifurcating orbits). Including only a few stable and
unstable orbits, we reproduce the quantum-mechanical density of states very
accurately. We also present a perturbative calculation of the stabilities of
two infinite series of orbits (R$_n$ and L$_m$), emanating from the shortest
librating straight-line orbit (A) in a bifurcation cascade just below the
barrier, which at the barrier have two common asymptotic Lyapunov exponents
$\chi_{\rm R}$ and $\chi_{\rm L}$.
