Nosé equation for a one-dimensional oscillator: Resonance zones and the transition to large-scale irregular dynamics

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Abstract
Recently, attempts have been made to alter the equation of motion of a multiparticle system so that the temperature rather than the energy is constant. Nosé introduced a modified multiparticle equation of motion involving an auxiliary equation with a free parameter Q. We consider the Nosé-Hoover equation for a one-dimensional oscillator as the equation of motion for a coupled oscillator system with two degrees of freedom. For different values of Q, we consider the dynamics in the four-dimensional phase space by examining two-dimensional surfaces of section. We show that the overlapping of resonance zones causes a transition to large-scale irregular dynamics for a limited range of Q.