Nose-Hoover dynamics of a nonintegrable Hamiltonian system

We study the dynamics of a hamiltonian system with two degrees of freedom coupled to a Nose-Hoover thermostat. In the absence of the thermostat, the system is quasi-integrable: at low energies, most of the motion is on two-dimensional tori, while at higher energies, the motion is mainly chaotic. Upon coupling to the thermostat the system becomes more chaotic, as evidenced by the magnitude of the largest Lyapunov exponent. In contrast to the case of isotropic oscillator systems coupled to thermostats, there is no evidence for a regime of integrable behaviour, even for large values of Q.