Conformal measures for rational functions revisited
Volume 157 / 1998
Fundamenta Mathematicae 157 (1998), 161-173
DOI: 10.4064/fm_1998_157_2-3_1_161_173
Abstract
We show that the set of conical points of a rational function of the Riemann sphere supports at most one conformal measure. We then study the problem of existence of such measures and their ergodic properties by constructing Markov partitions on increasing subsets of sets of conical points and by applying ideas of the thermodynamic formalism.
