×

Abelian integrals for a planar cubic non-Hamiltonian integrable system. (Chinese. English summary) Zbl 1264.34061

Summary: We study the lowest upper bound of the number of zeros of abelian integrals for a planar cubic non-Hamiltonian integrable system, when we perturb such a system inside the class of all polynomial systems of degree \(n\), and obtain that the lowest upper bound of the number of zeros of this abelian integral is \(n\).

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
14H70 Relationships between algebraic curves and integrable systems
37K99 Dynamical system aspects of infinite-dimensional Hamiltonian and Lagrangian systems
PDFBibTeX XMLCite