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?
2026-04-10 06:53:18.1775803998
When is the winding number undefined
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