Global bifurcation of limit cycles in a family of polynomial systems
The article is devoted to one of the weakened versions of Hilbert's 16th problem, the so-called infinitesimal Hilbert problem. This task is closely related to the problem of determining an upper bound for the number of limit cycles of the perturbed Hamiltonian system \(\dot{x}=H_y+\varepsilon P(x,y)\), \(\dot{y}=-H_x+\varepsilon Q(x,y)\). The authors give ane stimate on the number of limit cycles for a family of such polynomial systems.
scientific article; zbMATH DE number 2085958