Lyapunov exponents as a dynamical indicator of a phase transition

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We study analytically the behavior of the largest Lyapunov exponent λ₁ for a one-dimensional chain of coupled nonlinear oscillators, by combining the transfer integral method and a Riemannian geometry approach. We apply the results to a simple model, proposed for the DNA denaturation, which emphasizes a first order-like or second order phase transition depending on the ratio of two length scales: this is an excellent model to characterize λ₁ as a dynamical indicator close to a phase transition.