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首页> 外文期刊>Progress of Theoretical Physics >The renormalization-group method applied to asymptotic analysis of vector fields
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The renormalization-group method applied to asymptotic analysis of vector fields

机译：重归化群法在向量场渐近分析中的应用

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摘要

The renormalization group method of Goldenfeld, Oono and their collaborators is applied to the asymptotic analysis of vector fields. The method is formulated on the basis of the theory of envelopes, as was done for scalar fields. This formulation completes the discussion of the previous work for scalar equations. It is shown in a generic way that the method applied to equations with a bifurcation leads to the Landau-Stuart and (time-dependent) Ginzburg-Landau equations. It is confirmed that this method is actually a powerful theory for the reduction of dynamics as is the reductive perturbation method. Some examples for ordinary differential equations, such as the forced Duffing, the Lotka-Volterra and the Lorenz equations, are worked out in this method: The time evolution of the solution of the Lotka-Volterra equation is given explicitly, while the center manifolds of the Lorenz equation are constructed in a simple way using the RG method.
机译：将Goldenfeld，Oono及其合作者的重归一化组方法应用于矢量场的渐近分析。与标量场一样，该方法是根据包络理论制定的。此公式完成了对标量方程先前工作的讨论。以一般的方式表明，该方法应用于具有分支的方程组会导致Landau-Stuart和（随时间变化的）Ginzburg-Landau方程组。可以肯定的是，与还原摄动法一样，该方法实际上是减少动力学的有力理论。用这种方法算出了一些常微分方程的例子，例如强制Duffing方程，Lotka-Volterra方程和Lorenz方程：明确给出了Lotka-Volterra方程解的时间演化，同时给出了中心流形。使用RG方法以简单的方式构造Lorenz方程。

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