  We consider oscillators evolving subject to a periodic driving force that
dynamically entangles them, and argue that this gives the linearized evolution
around periodic orbits in a general chaotic Hamiltonian dynamical system. We
show that the entanglement entropy, after tracing over half of the oscillators,
generically asymptotes to linear growth at a rate given by the sum of the
positive Lyapunov exponents of the system. These exponents give a classical
entropy growth rate, in the sense of Kolmogorov, Sinai and Pesin. We also
calculate the dependence of this entropy on linear mixtures of the oscillator
Hilbert space factors, to investigate the dependence of the entanglement
entropy on the choice of coarse-graining. We find that for almost all choices
the asymptotic growth rate is the same.
