论文标题
一类普通微分方程的重新归一化组理论扰动的评论
A remark on renormalization group theoretical perturbation in a class of ordinary differential equations
论文作者
论文摘要
我们重新审视振荡器型二阶平方方程的重新归一化组（RG）理论扰动理论。对于一类电位，我们在幼稚的扰动系列中显示了谐波的世俗系数之间的简单功能关系。它导致裸露和重新归一化幅度之间的反演公式，以及在RG系列的所有顺序中都没有世俗项的基本证明。结果涵盖了非自主和自主病例，并完善了早期的研究，包括范德尔Pol，Mathieu，Duffing和Rayleigh方程的经典例子。
We revisit the renormalization group (RG) theoretical perturbation theory on oscillator-type second-order ordinary differential equations. For a class of potentials, we show a simple functional relation among secular coefficients of the harmonics in the naive perturbation series. It leads to an inversion formula between bare and renormalized amplitudes and an elementary proof of the absence of secular terms in all orders of the RG series. The result covers nonautonomous as well as autonomous cases and refines earlier studies, including the classic examples of Van der Pol, Mathieu, Duffing, and Rayleigh equations.
