On the Poincaré–Lyapunov constants and the Poincaré series. (English) Zbl 1022.34028
For an arbitrary analytic system with a linear center at the origin, all Poincaré-Lyapunov constants in terms of the coefficients are recursively calculated. The coefficients of the Poincaré series in terms of the same coefficients are also computed. The algorithm for these computations is applied to some polynomial differential systems.
Reviewer: Ruyun Ma (Lanzhou)
MSC:
| 34C05 | Topological structure of integral curves, singular points, limit cycles of ordinary differential equations |
| 34A34 | Nonlinear ordinary differential equations and systems |
| 34C25 | Periodic solutions to ordinary differential equations |
