Covariant hydrodynamic Lyapunov modes and strong stochasticity threshold   in Hamiltonian lattices
  We scrutinize the reliability of covariant and Gram-Schmidt Lyapunov vectors for capturing hydrodynamic Lyapunov modes (HLMs) in one-dimensional Hamiltonian lattices. We show that,in contrast with previous claims, HLMs do exist for any energy density, so that strong chaos is not essential for the appearance of genuine (covariant) HLMs. In contrast, Gram-Schmidt Lyapunov vectors lead to misleading results concerning the existence of HLMs in the case of weak chaos. 
M. Romero-Bastida, Diego Paz\'o, Juan M. L\'opez
nlin.CD