On the number of critical periods for planar polynomial systems (Q944752)

The authors consider planar polynomial systems and get some lower bounds of critical periods for families of centers which are perturbations of the linear one. They present a method which lets them prove that there are polynomial centers of degree \(l\) with at least \(2[(l-2)/2]\) critical periods, moreover they study concrete families of potential, reversible, and Liénard centers. The last case is studied in more detail; in particular, it is proved that the number of critical periods obtained with the authors' approach does not increase with the order of the perturbation.