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.
Every period annulus is both reversible and symmetric / Sabatini, Marco. - In: QUALITATIVE THEORY OF DYNAMICAL SYSTEMS. - ISSN 1575-5460. - 2017, 16:(2017), pp. 175-185. [10.1007/s12346-015-0183-7]
Every period annulus is both reversible and symmetric
Sabatini, Marco
2017-01-01
Abstract
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.| File | Dimensione | Formato | |
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Sabatini Marco - Every Period Annulus is Both Reversible and Symmetric.pdf
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