The monotonicity and convexity of the period function for a class of symmetric Newtonian systems of degree ۸

In this paper, we study the monotonicity and convexity of the period function associated with centers of a specific class of symmetric Newtonian systems of degree ۸. In this regard, we prove that if the period annulus surrounds only one elementary center, then the corresponding period function is monotone; but, for the other cases, the period function has exactly one critical point. We also prove that in all cases, the period function is convex.

Keywords:

. Newtonian system , Period function , Monotonicity