作为约束线性系统的共振规范形
Resonant normal forms as constrained linear systems
摘要：
我们表明，Poincare '-Dulac规范型（在$\R^n$）的非线性动力系统可以被看作是一个约束线性系统;的限制是由共振条件所满足的频谱（的线性部分）的系统，并确定一个自然不变的流形的流动的“父”的线性系统。如果谱仅满足有限数量的共振条件，则母系统是有限维的，如庞加莱条件所暗示的。在这种情况下，我们的结果可以用来整合共振正规形，并揭示了霍恩，Lyapounov和Dulac的经典集成方法背后的几何。
英文摘要：
We show that a nonlinear dynamical system in Poincare'-Dulac normal form (in $\R^n$) can be seen as a constrained linear system; the constraints are given by the resonance conditions satisfied by the spectrum of (the linear part of) the system and identify a naturally invariant manifold for the flow of the ``parent'' linear system. The parent system is finite dimensional if the spectrum satisfies only a finite number of resonance conditions, as implied e.g. by the Poincare' condition. In this case our result can be used to integrate resonant normal forms, and sheds light on the geometry behind the classical integration method of Horn, Lyapounov and Dulac.
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