On the period function of reversible quadratic centers with their orbits inside quartics
The authors study the monotonicity of the period function for the planar real system (belonging to the class of reversible quadratic centers) of the form: \[ \dot x = y + 8(b+1)xy, \quad \dot y = -x -2(3b+1)x^2 + 6(b+1)y^2, \] where \(b \neq -1\) is a real number. In particular, they prove that such system has a period function with at most one critical point.
scientific article; zbMATH DE number 5612991
scientific article