Fang, Qigui The number of limit cycles of a kind of isochronous system. (Chinese. English summary) Zbl 1474.34234 J. Northwest Norm. Univ., Nat. Sci. 56, No. 5, 18-21 (2020). Summary: For a kind of quadratic system \(\dot x = -y+{x^2}-{y^2},\; \dot y = x+2xy\) with isochronous centers, the upper bound of the number of limit cycles of this system is obtained under arbitrary real polynomial perturbations of degree \(n\) by using abelian integral and Picard-Fuchs equation. MSC: 34C07 Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert’s 16th problem and ramifications) for ordinary differential equations 34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations 34C23 Bifurcation theory for ordinary differential equations Keywords:isochronous system; limit cycle; abelian integral; Picard-Fuchs equation PDFBibTeX XMLCite \textit{Q. Fang}, J. Northwest Norm. Univ., Nat. Sci. 56, No. 5, 18--21 (2020; Zbl 1474.34234) Full Text: DOI