Algebraic limit cycles for quadratic polynomial differential systems
The paper deals with the question about the maximal number of algebraic limit cycle as a weakened version of the second part of Hilbert's 16th problem. For quadratic planar autonomous systems the conjecture is well-known that such systems have at most one algebraic limit cycle. The authors provide a positive answer to this conjecture in a new case when the quadratic system has three pairs of diametrally opposite equilibrium points at infinity that are positively rationally independent, in other words, the Jacobian matrix of the differential equation at each of these points has two eigenvalues \(\lambda \neq 0\), \(\mu \neq 0\) such that \(\lambda/\mu \) is not a positive rational number.
quadratic polynomial differential system
scientific article; zbMATH DE number 6994970
scientific article