204 Progress of Theoretical Physics Supplement No. 139, 2000 Chaos in the Thermodynamic Limit

We study chaos in the Hamiltonian Mean Field model (HMF), a system with many degrees of freedom in which N classical rotators are fully coupled. We review the most important results on the dynamics and the thermodynamics of the HMF, and in particular we focus on the chaotic properties. We study the Lyapunov exponents and the Kolmogorov-Sinai entropy, namely their dependence on the number of degrees of freedom and on energy density, both for the ferromagnetic and the antiferromagnetic case. In systems with a few degrees of freedom the Largest Lyapunov Exponent (LLE), which quantifies chaotic motion, is often studied as a function of the control param-eter. In many-degrees-of-freedom systems, this can also be done and, moreover, the control parameter may acquire a more transparent physical meaning, making refer