{"title":"Simultaneity of centres in double-reversible planar differential systems","authors":"J. Giné, C. Valls","doi":"10.1080/14689367.2020.1853061","DOIUrl":null,"url":null,"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.","PeriodicalId":50564,"journal":{"name":"Dynamical Systems-An International Journal","volume":"36 1","pages":"167 - 180"},"PeriodicalIF":0.5000,"publicationDate":"2020-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/14689367.2020.1853061","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Dynamical Systems-An International Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1080/14689367.2020.1853061","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 1
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.
期刊介绍：
Dynamical Systems: An International Journal is a world-leading journal acting as a forum for communication across all branches of modern dynamical systems, and especially as a platform to facilitate interaction between theory and applications. This journal publishes high quality research articles in the theory and applications of dynamical systems, especially (but not exclusively) nonlinear systems. Advances in the following topics are addressed by the journal:
•Differential equations
•Bifurcation theory
•Hamiltonian and Lagrangian dynamics
•Hyperbolic dynamics
•Ergodic theory
•Topological and smooth dynamics
•Random dynamical systems
•Applications in technology, engineering and natural and life sciences
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