Ergodic Theory and Dynamical Systems



Bounded hyperbolic components of quadratic rational maps


ADAM LAWRENCE EPSTEIN a1
a1 Department of Mathematics, Cornell University, Ithaca, NY 14853-4201, USA (e-mail: adame@math.cornell.edu)

Abstract

Let $\mathcal{H}$ be a hyperbolic component of quadratic rational maps possessing two distinct attracting cycles. We show that $\mathcal{H}$ has compact closure in moduli space if and only if neither attractor is a fixed point.

(Received September 20 1997)
(Revised June 4 1999)