  We consider the links between nonlinear dynamics and thermodynamics in the
framework of a simple nonlinear model for DNA. Two analyses of the phase
transition, either with the transfer integral approach or by considering the
instability of a nonlinear particular solution, are discussed. Conversely, the
computation of the largest Lyapunov exponent is obtained within a thermodynamic
treatment. Differences with the Peyrard-Bishop model are also discussed.
