We perform a global dynamical analysis of a modified Nosé-Hoover oscillator, obtained as the perturbation of an integrable differential system. Using this new approach for studying such an oscillator, in the integrable cases, we give a complete description of the solutions in the phase space, including the dynamics at infinity via the Poincaré compactification. Then using the averaging theory, we prove analytically the existence of a linearly stable periodic orbit which bifurcates from one of the infinite periodic orbits which exist in the integrable cases. Moreover, by a detailed numerical study, we show the existence of nested invariant tori around the bifurcating periodic orbit. Finally, starting with the integrable cases and increasing the parameter values, we show that chaotic dynamics may occur, due to the break of such an invariant tori, leading to the creation of chaotic seas surrounding regular regions in the phase space.

我们对改进的Nosé-Hoover振荡器进行了全局动力学分析，该振荡器是由可积分微分系统的扰动获得的。在可积情况下，使用这种新方法研究此类振荡器，我们对相空间中的解决方案进行了完整描述，包括通过庞加莱压实实现的无限远处的动力学。然后，使用平均理论，我们分析地证明了线性稳定周期轨道的存在，该周期分支与可积情况下存在的无限周期轨道之一分叉。此外，通过详细的数值研究，我们证明了分叉周期轨道周围存在嵌套不变托里的存在。最后，从可积情况开始并增加参数值，我们表明由于这种不变的环面的破裂，可能会发生混沌动力学，