Journal of Approximation Theory vol:184 pages:28-54
We study the limiting zero distribution of orthogonal polynomials with respect to some particular exponential weights exp(-nV(z)) along contours in the complex plane. We are especially interested in the question under which circumstances the zeros of the orthogonal polynomials accumulate on a single analytic arc (one cut case), and in which cases they do not. In a family of cubic polynomial potentials , we determine the precise values of K for which we have the one cut case. We also prove the one cut case for a monomial quintic on a contour that is symmetric in the imaginary axis.