Analytic Lyapunov exponents in a classical nonlinear field equation

It is shown that the nonlinear wave equation [Formula Presented] which is the continuum limit of the Fermi-Pasta-Ulam [Formula Presented] model, has a positive Lyapunov exponent [Formula Presented] whose analytic energy dependence is given. The result (a first example for field equations) is achieved by evaluating the lattice-spacing dependence of [Formula Presented] for the FPU model within the framework of a Riemannian description of Hamiltonian chaos. We also discuss a difficulty of the statistical mechanical treatment of this classical field system, which is absent in the dynamical description. © 2000 The American Physical Society.