# The monotonicity and convexity of the period function for a class of symmetric Newtonian systems of degree 8

Document Type : Research Paper

Authors

1 Department of Mathematical Sciences, University of Kashan, Kashan, 87317-53153, Iran.

2 Department of Mathematics, Yazd University, Yazd, 89195-741 Iran.

Abstract

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 8. 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

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### History

• Receive Date: 13 August 2020
• Revise Date: 10 December 2020
• Accept Date: 12 December 2020
• First Publish Date: 05 January 2021