Global characterization of the normal form for a vector field near a closed orbit
A simple global characterization of normal forms for vector fields near a singularity was given recently by \textit{C. Elphick}, \textit{E. Tirapegui}, \textit{M. Brachet}, \textit{P. Coullet}, and the author [Physica D 29, 95-127 (1987; Zbl 0633.58020)]. In this paper, the author derives a natural generalization of this global characterization for vector fields near a closed orbit. The global characterization presented here separates the time law for the phase along the closed curve and the transverse dynamics in terms of this phase. This is expressed by a natural extension of the characterization obtained in the autonomous case, again in a constructive way.
scientific article; zbMATH DE number 4071973
scientific article