On the self-intersections of the image of the unit circle under a polynomial mapping

Abstract

We prove that if $p$ is a polynomial of degree $n$, then with certain exceptions the image of the unit circle under the mapping $p$ has at most ${(n - 1)^2}$ points of self-intersection. We apply our method to the problem of computing polynomials univalent in $|z| < 1$.

Locations

• Proceedings of the American Mathematical Society - View - PDF