Simultaneity of centres in double-reversible planar differential systems. Issue 1 (2nd January 2021)

• Record Type: Journal Article
• Authors: Giné, Jaume; Valls, Claudia
• Is Part Of: Dynamical systems. Volume 36:Issue 1(2021)
• Page Start: 167
• Page End: 180
• Publication Date: 2021-01-02
• Subjects: Reversible system -- centre-focus problem -- simultaneity of centres -- first integrals -- crossed resultants; 34C05 -- 34A34 -- 34C14; Differentiable dynamical systems -- Periodicals; 515.35205
• DOI: 10.1080/14689367.2020.1853061
• Languages: English
• ISSNs: 1468-9367

Abstract

ABSTRACT: We provide the sufficient conditions for the simultaneous existence of centres for two families of planar double-reversible quintic systems. Computing the focal values and using crossed resultants and Gröbner bases, we find the centre conditions for such systems. The results obtained show that there exist a kind of symmetry where the number of centers in a quintic system is more than 5, so higher than the degree of the system. This fact gives a counterexample to the question posed in a previous work.