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Ali Taghavi
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The centroid of the interior of level sets of a two variable polynomial function whose eventual level sets are simple closed curve

Is there a polynomial function $P:\mathbb{R}^2 \to \mathbb{R}$ with the following property?: For sufficiently large $c>0$, $P^{-1}(c)$ is a simple closed curve $\gamma_c$ but the centroid $e_c$ of the interior of $\gamma_c$ does not converge to any point of $\mathbb{R}^2$ as $c$ goes to $+\infty$

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