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April  2005, 13(3): 795-810. doi: 10.3934/dcds.2005.13.795

On the monotonicity of the period function of a quadratic system

Yulin Zhao 1,

1. 

Department of Mathematics, Sun Yat-sen University, Guangzhou, 510275

Received  November 2004 Revised  April 2005 Published  May 2005

In this paper, we study the monotonicity of the period function of the quadratic system

$ \dot x=- y + x y,\quad \dot y=x + 2 y^2-c x^2, \quad -\infty < c < +\infty.$

We show that this system has two isochronous centers for $c=1/2$, and its period function has only one critical point for $c\in(7/5, 2)$. For all other cases, the period function is monotone. This improves the results in [1].

Keywords: Period function, the critical points., Picard-Fuchs equations.
Mathematics Subject Classification: 34C07, 34C08, 37G1.
Citation: Yulin Zhao. On the monotonicity of the period function of a quadratic system. Discrete & Continuous Dynamical Systems, 2005, 13 (3) : 795-810. doi: 10.3934/dcds.2005.13.795
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