descriptionPublicationkeyboard_double_arrow_right Article 12 May 2018 English Publisher:Springer Science and Business Media LLCJournal:Journal of Dynamics and Differential Equations, volume 30, pages 1,295-1,310 (issn: 1040-7294, eissn: 1572-9222,

Authors: Jaume Llibre; Rafael Ramírez; Valentín Ramírez; Natalia Sadovskaia;

doi: 10.1007/s10884-018-9672-0

handle: 2117/122773

Centers and Uniform Isochronous Centers of Planar Polynomial Differential Systems

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Abstract

For planar polynomial vector fields of the form \[ (-y X(x,y)) x (x Y(x,y)) y, \] where X and Y start at least with terms of second order in the variables x and y, we determine necessary and sufficient conditions under which the origin is a center or a uniform isochronous centers.

Related Organizations

Universitat Polite`cnica de Catalunya
Spain
University of Barcelona
Spain
Universitat Politècnica de Catalunya
Spain
Autonomous University of Barcelona
Spain
Universitat Rovira i Virgili
Spain

Keywords

Differential equations, :34 Ordinary differential equations::34C Qualitative theory [Classificació AMS], Classificació AMS::34 Ordinary differential equations::34C Qualitative theory, Center-focus problem, Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Equacions diferencials ordinàries, :Matemàtiques i estadística::Equacions diferencials i integrals::Equacions diferencials ordinàries [Àrees temàtiques de la UPC], Equacions diferencials ordinàries, Polynomial planar differential system, Uniform isochronous centers

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