Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8899308 | Journal of Mathematical Analysis and Applications | 2018 | 16 Pages |
Abstract
We say that a polynomial differential system xË=P(x,y), yË=Q(x,y) having the origin as a singular point is Z2-symmetric if P(âx,ây)=âP(x,y) and Q(âx,ây)=âQ(x,y). It is known that there are nilpotent centers having a local analytic first integral, and others which only have a Câ first integral. However these two kinds of nilpotent centers are not characterized for different families of differential systems. Here we prove that the origin of any Z2-symmetric system is a nilpotent center if, and only if, there is a local analytic first integral of the form H(x,y)=y2+â¯, where the dots denote terms of degree higher than two.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Antonio Algaba, Cristóbal GarcÃa, Jaume Giné, Jaume Llibre,