Analytic Lyapunov exponents in a classical nonlinear field equation

It is shown that a nonlinear wave equation which is the continuum limit of the Fermi- Pasta-Ulam (FPU) β model, has a positive Lyapunov expo- nent λ1, whose analytic energy dependence is given. The result (a first example for field equations) is achieved by evaluating the lattice-spacing dependence of λ1 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.