On Deficiencies of Differential Polynomials, II.
Using a result due to M. Shub, a theorem about the existence of fixed points inside the unit disc for extensions of expanding maps defined on the boundary is established. An application to a special class of rational maps on the Riemann sphere and some considerations on ergodic properties of these maps are also made.
A criterion for the existence of fixed point of one-dimensional holomorphic maps is established.