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We study the one-dimensional discrete $\Phi^4$ model. We compare twoequilibrium properties by use of molecular dynamics simulations: the Lyapunovspectrum and the time dependence of local correlation functions. Bothproperties imply the existence of a dynamical crossover of the system at thesame temperature. This correlation holds for two rather different regimes ofthe system - the displacive and intermediate coupling regimes. Our resultsimply a deep connection between slowing down of relaxations and phase spaceproperties of complex systems.Comment: 14 pages, LaTeX, 10 Figures available upon request (SF), Phys. Rev.  E, accepted for publicatio

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