Universitat de Lleida
    • English
    • català
    • español
  • English 
    • English
    • català
    • español
  • Login
Repositori Obert UdL
View Item 
  •   Home
  • Recerca
  • Matemàtica
  • Articles publicats (Matemàtica)
  • View Item
  •   Home
  • Recerca
  • Matemàtica
  • Articles publicats (Matemàtica)
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

Centers for the Kukles homogeneous systems with odd degree

Thumbnail
View/Open
Postprint (115.8Kb)
Issue date
2015
Author
Giné, Jaume
Llibre, Jaume
Valls, Claudia
Suggested citation
Giné, Jaume; Llibre, Jaume; Valls, Claudia; . (2015) . Centers for the Kukles homogeneous systems with odd degree. Bulletin of the London Mathematical Society, 2015, vol. 47, p. 315-324. https://doi.org/10.1112/blms/bdv005.
Impact


Web of Science logo    citations in Web of Science

Scopus logo    citations in Scopus

Google Scholar logo  Google Scholar
Share
Export to Mendeley
Metadata
Show full item record
Abstract
For the polynomial differential system x˙ = −y, y˙ = x+Qn(x; y), where Qn(x; y) is a homogeneous polynomial of degree n there are the following two conjectures done in 1999. (1) Is it true that the previous system for n ≥ 2 has a center at the origin if and only if its vector field is symmetric about one of the coordinate axes? (2) Is it true that the origin is an isochronous center of the previous system with the exception of the linear center only if the system has even degree? We prove both conjectures for all n odd.
URI
http://hdl.handle.net/10459.1/58395
DOI
https://doi.org/10.1112/blms/bdv005
Is part of
Bulletin of the London Mathematical Society, 2015, vol. 47, p. 315-324
European research projects
Collections
  • Publicacions de projectes finançats per la Unió Europea [537]
  • Publicacions de projectes de recerca del Plan Nacional [2180]
  • Articles publicats (Matemàtica) [264]

Related items

Showing items related by title, author, creator and subject.

  • Centers for the Kukles homogeneous systems with even degree 

    Giné, Jaume; Llibre, Jaume; Valls, Claudia (Shanghai Normal University & Wilmington Scientific Publisher, 2017)
    For the polynomial differential system x˙=−y, y˙=x+Qn(x,y), where Qn(x,y) is a homogeneous polynomial of degree n there are the following two conjectures done in 1999. (1) Is it true that the previous system for n≥2 has a ...
  • Centers for generalized quintic polynomial differential systems 

    Giné, Jaume; Llibre, Jaume; Valls, Claudia (Rocky Mountain Mathematics Consortium, 2017)
    We classify the centers of polynomial differential systems in $R^2$ of odd degree $d \ge 5$, in complex notation, as $\dot{z} = iz + (z \bar z)^(d-5)/2(A z^5 + B z^4 \bar z + C z^3 \bar z^2 + D z^2 \bar z^3 + E z \bar z^4 ...
  • Chiellini Hamiltonian Liénard differential systems 

    Giné, Jaume; Llibre, Jaume; Valls, Claudia (Texas State University, 2019)
    We characterize the centers of the Chiellini Hamiltonian Li´enard second-order differential equations x 0 = y, y 0 = −f(x)y − g(x) where g(x) = f(x)(k − α(1 + α) R f(x)dx) with α, k ∈ R. Moreover we study the ...

Contact Us | Send Feedback | Legal Notice
© 2021 BiD. Universitat de Lleida
Metadata subjected to 
 

 

Browse

All of the repositoryCommunities & CollectionsBy Issue DateAuthorsTitlesSubjectsThis CollectionBy Issue DateAuthorsTitlesSubjects

Statistics

View Usage Statistics

D'interès

Política institucional d'accés obertDiposita les teves publicacionsDiposita dades de recercaSuport a la recerca

Contact Us | Send Feedback | Legal Notice
© 2021 BiD. Universitat de Lleida
Metadata subjected to