  We calculate the maximal Lyapunov exponent for a bulk system of 256
Lennard-Jones particles in constant energy molecular dynamics simulations deep
into the supercritical state. We find that the maximal Lyapunov exponent
undergoes a crossover, and that this crossover coincides with the dynamical
crossover at the Frenkel line from liquid physics. We explain this crossover in
terms of two different contributions to dynamical instability: diffusion in the
liquid-like state below the Frenkel line, and collisions in the gas-like state
above. These results provide insight into the phase space dynamics far from the
melting line and densities where rare-gas approximation are inapplicable.
