Chaos in the thermodynamic limit

We study chaos in the Hamiltonian Mean Field model (HMF), a system with man y degrees of freedom in which N classical rotators are fully coupled. We re view the most important results on the dynamics and the thermodynamics of t he HMF, and in particular we focus on the chaotic properties. We study the Lyapunov exponents and the Kolmogorov-Sinai entropy, namely their dependenc e on the number of degrees of freedom and on energy density, both for the f erromagnetic and the antiferromagnetic case.