regard to averaging, the methods developed by Krylov, Bogoliuv and Mitropol- sky can be shown a special case of the transformation groups introduced by Sophus Lie [Cohn65, Firk00]. His theory of near-identity transformations provides a solid the- oretical basis for higher-order averaging methods. Here, we also mention the theory of manifolds, tangent spaces and integration on manifolds [Abra88]. These concepts are important in the theory of differential algebraic equations and model-order reduction. The analysis of the nonlinear van der Pol oscillator by Balthazar van der Pol [Vand20] is probably one of the first studies on the behavior of nonlinear electronic oscillators. Many authors have followed his lead [Bogo61, Buo02, Chua92, Guck80, Murd88, Rob83, Stav00, Sto50]5. Hereby, describing function analysis [Gelb68, Kha96, Lee98] and singular perturbation theory [Kha96] are among the most frequently used tech- niques for analyzing an oscillator's behavior. However, these methods are often tailored to the needs of a particular application, i.e a particular set of differential equations. Hence, they lack generality. Handling a set of equations extracted from an oscillator circuit netlist remains an open problem. 5.2.2 Phase noise analysis Among the work on nonlinear oscillator behavior, we highlight the oscillator phase noise theories developed in recent years [Cran98, Dem00a, Dem00b, Dem02, Demu02, Haji98, Kae90, Lees66]. These theories study the impact of noisy disturbances on an oscillator's phase behavior. Fig. 5.8(a) illustrates the well-known impact noise has on the oscillator's power spectral density (PSD). Phase noise causes the energy contained in the oscillating signal to spread over the frequency band. This spectral spreading is, typically, characterized by a flat close-in phase-noise PSD followed by an 1/f3 region (due to upconverted 1/f input noise) and an 1/f2 region (due to white input noise). The most rigorous treatments on phase noise analysis are given in [Dem00a, Dem00b, Dem02, Kae90]. Here, the 