  The Hamiltonian dynamics of chains of nonlinearly coupled particles is
numerically investigated in two and three dimensions. Simple, off-lattice
homopolymer models are used to represent the interparticle potentials. Time
averages of observables numerically computed along dynamical trajectories are
found to reproduce results given by the statistical mechanics of homopolymer
models. The dynamical treatment, however, indicates a nontrivial transition
between regimes of slow and fast phase space mixing. Such a transition is
inaccessible to a statistical mechanical treatment and reflects a bimodality in
the relaxation of time averages to corresponding ensemble averages. It is also
found that a change in the energy dependence of the largest Lyapunov exponent
indicates the theta-transition between filamentary and globular polymer
configurations, clearly detecting the transition even for a finite number of
particles.
