Resumen de Elliptic Functions With Critical Points Eventually Mapped Onto Infinity

Janina Kotus

• We consider the class of elliptic functions whose critical points in the Julia set are eventually mapped onto 8. This paper is a continuation of our previous papers, namely [11] and [12]. We study the geometry and ergodic properties of this class of elliptic functions. In particular, we obtain a lower bound on the Hausdorff dimension of the Julia set that is bigger than the estimate proved in [11]. Let h be the Hausdorff dimension of the Julia set of f. We construct an atomless h-conformal measure m and prove the existence of a (unique up to a multiplicative constant) s-finite f-invariant measure µ equivalent to m. The measure µ is ergodic and conservative