Geometry and ergodic theory of conformal non-recurrent dynamics

摘要

Lct h be the Hausdorff dimension of the Julia set of a rational function T with no non-periodic recurrenl critical poinls and let .in be the only h-conformal measure for T. We prove Ihe existence of a o-finite h-invariant measure h equivalent will) m. The uieasure h is then proved to be ergodic and conservative and we study the set of those points whose all open neighborhoods have infinite measure ft. Developing the concept e inverse jump trans formation wo show that the packing and Hausdorff dimensions ithe con formal measure are equal to h. We also provide some sufficient conditions for iusdoiff and box dimensions of the Julia sei to be equal.