Resumen de Every Period Annulus is Both Reversible and Symmetric

Marco Sabatini

• We prove that for every planar differential system with a period annulus there exists a unique involution σ such that the system is σ-symmetric. We also prove that, given a system with a period annulus and a global section δ, there exist a unique involution σ such that the system is σ-reversible and δ is the fixed points curve of σ. As a consequence, every system with a period annulus admits infinitely many reversibilities.