Normal forms
We consider an autonomous system of ordinary differential equations near its stationary point. By means of the formal change of coordinates, we can transform the system into its normal form. By means of the power transformation of coordinates, the normal form is reduced to a problem of less dimension. Here we compare two kinds of normal forms: resonant and Belitskii. We discuss methods of their computation and point out a new property which simplifies computation of the Belitskii normal form. We apply this approach to study periodic solutions of the Henon-Heiles system.
ordinary differential equations computation belitskii normal form resonant normal form