On hausdorff measures and sbr measures for parabolic rational maps

摘要

If J is the Julia set of a parabolic rational map having Hausdorff dimension h < 1, we show that Sullivan's h-conformal measure on J is either absolutely continuous of orthogonal with respect to the Hausdorff measures defined by the function f(t) = t~h(log1/t)~(#tau#), according to whether #tau# > #tau#_0 or #tau# <= #tau#_0 for some explicitly computable #tau#_0 > 0.