Slow relaxation and phase space properties of a conservative system with many degrees of freedom.

The object of our study is the one-dimensional discrete Φ 4 model. We compare two equilibrium properties by use of molecular dynamics simulations: the Lyapunov spectrum and the time dependence of displacement-displacement and energy-energy correlation functions. Both properties imply the existence of a dynamical crossover of the system at the same temperature. This correlation holds for two rather different regimes of the system-the displacive and intermediate coupling regimes. These results imply a deep connection between slowing down of relaxations and phase space properties of complex systems.