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Let $\phi_R(t)=R(\cos 2t + i\sin 2t)$ be the closed circle of radius $R \geq 0$ going twice around the origin. Consider the closed curve $P_R(t)=p(\phi_R(t))$, where $p(z)$ is the polynomial $z^3+z^2-2z-2$. What is the smallest $R>0$ for which the winding number of $P_R(t)$ is undefined?

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    $\begingroup$ Winding number with respect to which point? $\endgroup$ – Christian Blatter Nov 10 '18 at 14:24
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    $\begingroup$ If $R^2=2$ the curve degenerates to a point. $\endgroup$ – Michael Hoppe Nov 10 '18 at 15:09

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