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# On the monotonicity of the period function of a quadratic system

• 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].

Mathematics Subject Classification: 34C07, 34C08, 37G15.

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