Chaoticity spectrum in Hamiltonian systems with many degrees of freedom

We present a diagnostic tool to analyze the chaoticity of single degrees of freedom: the coherence angles, which measure the angular distance between any physically relevant direction and the direction of maximum expansion in the tangent space. They allow at the same time a detailed characterization and a synoptic view of the dynamical behavior of a system with many degrees of freedom. Results are presented for two- and three-dimensional Lennard-Jones lattices, which show a nontrivial structure of the spectrum of coherence angles.