Ergodic Theory and Dynamical Systems

Convergence of the transfer operator for rational maps

a1 Mathematics Department, University of Southern California, Los Angeles, 90089-1113, USA (e-mail:


We prove that the transfer operator for a general class of rational maps converges exponentially fast in the supremum norm and in Hölder norms, for small enough Hölder exponents, to its principal eigendirection.

(Received April 10 1997)
(Revised March 20 1998)