Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5774053 | Journal of Differential Equations | 2017 | 43 Pages |
Abstract
We study the particular case of centers which have a local analytic first integral of the form H=12(x2+y2)(1+âj=1âÏj), in a neighborhood of the origin, where Ïj is a convenient homogenous polynomial of degree j, for jâ¥1. These centers are called weak centers, they contain the class of center studied by Alwash and Lloyd, the uniform isochronous centers and the isochronous holomorphic centers, but they do not coincide with the class of isochronous centers. We give a classification of the weak centers for quadratic and cubic vector fields with homogenous nonlinearities.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Jaume Llibre, Rafael RamÃrez, ValentÃn RamÃrez,