Obstructions for the linearization of polynomial vector fields. (Obstruction à la linéarisation des champs de vecteurs polynomiaux.) (French) Zbl 1016.37028
Summary: We characterize a class of polynomial vector fields which are not analytically linearizable using the correction introdcued by Écalle-Vallet. Then, we extend Schuman’s result about nonexistence of isochronous homogeneous Hamiltonian systems.
MSC:
| 37J30 | Obstructions to integrability for finite-dimensional Hamiltonian and Lagrangian systems (nonintegrability criteria) |
| 34D30 | Structural stability and analogous concepts of solutions to ordinary differential equations |
| 37G05 | Normal forms for dynamical systems |
| 34D10 | Perturbations of ordinary differential equations |
