Every Period Annulus is Both Reversible and Symmetric

• Marco Sabatini ^[1]
  1. [1] Università di Trento (Italia)
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 16, Nº 1, 2017, págs. 175-185
• Idioma: inglés
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• Resumen

  • 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.