New lower bound for the number of critical periods for planar polynomial systems

In this paper, we construct two classes of planar polynomial Hamiltonian systems having a center at the origin, and obtain lower bounds for number critical periods these systems. For potential degree n, provide bound n?2 periods, acquire n2/2+n?5/2 when n is odd n2/2?2 even periods. To best our knowledge, are new, moreover latter one twice existing results up to dominant term.