Lyapunov exponents as a dynamical indicator of a phase transition

We study analytically the behavior of the largest Lyapunov exponent lambda (1) for one-dimensional chain of coupled nonlinear oscillators, by combinin g the transfer integral method and Riemannian geometry approach. We apply t he results to simple model, proposed for the DNA denaturation, which emphas izes first-order like or second-order phase transition depending on the rat io of two length scales: this is an excellent model to characterize lambda (1) as dynamical indicator close to phase transition.