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On the monotonicity of the period function of a quadratic system
| 1. | Department of Mathematics, Sun Yat-sen University, Guangzhou, 510275 |
$ \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].
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