VARIATION OF HAUSDORFF DIMENSION OF JULIA SETS

Let (R(lambda))lambda is-an-element-of D be an analytic family of rational maps of degree d greater-than-or-equal-to 2, where D is a simply connected domain in C, and each R, is hyperbolic. Then the Hausdorff dimension delta(lambda) of the Julia set of R(lambda) satisfies [GRAPHICS] where H is a collection of harmonic functions u on D. We examine some consequences of this, and show how it can be used to obtain estimates for the Hausdorff dimension of some particular Julia sets.