Weak centers and bifurcation of critical periods in reversible cubic systems (Q1591917)

This paper is concerned with planar reversible cubic differential systems with a center. An inductive algorithm to compute the period coefficients is developed. Using a computer algebra program, the algorithm is applied to study the order of the period function at the origin. The following systems are studied in more detail, \[ \dot x= -y- ax^2+ ay^2+ a_3 x^2 y+ a_4 y^3,\quad \dot y= x- 2axy+ b_2 x^3+ b_3 xy^2. \] In their main result, the authors prove that, for \(j= 1,\dots, 4\), there exists such a system having \(j\) critical periods.