Centers and uniform isochronous centers of planar polynomial differential systems

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.

Bibliographic Details
Authors: Llibre Saló, Jaume, Ramirez Inostroza, Rafael, Ramírez Sadovski, Valentín, Sadovskaia Nurimanova, Natalia Guennadievna
Format: article
Publication Date:2018
Country:España
Institution:Universitat Politècnica de Catalunya (UPC)
Repository:UPCommons. Portal del coneixement obert de la UPC
Language:English
OAI Identifier:oai:upcommons.upc.edu:2117/122773
Online Access:https://hdl.handle.net/2117/122773
https://dx.doi.org/10.1007/s10884-018-9672-0
Access Level:Open access
Keyword:Differential equations
Center-focus problem
Polynomial planar differential system
Uniform isochronous centers
Equacions diferencials ordinàries
Classificació AMS::34 Ordinary differential equations::34C Qualitative theory
Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Equacions diferencials ordinàries
Description
Summary: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.