STEFAN GÜTTEL, GEORGES KLEIN, CONVERGENCE OF LINEAR BARYCENTRIC RATIONAL INTERPOLATION FOR ANALYTIC FUNCTIONS, SIAM Journal on Numerical Analysis, Vol. 50, No. 5 (2012), pp. 2560-2580 ...

This is equivalent to the following result: If all critical points of a rational function lie on a circle in the Riemann sphere (for example, on the real line), then the function maps this circle into ...