Elliptic Functions With Critical Points Eventually Mapped Onto Infinity

• Autores: Janina Kotus
• Localización: Monatshefte für mathematik, ISSN 0026-9255, Vol. 149, Nº 2, 2006, págs. 103-117
• Idioma: inglés
• DOI: 10.1007/s00605-005-0373-5
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• Resumen

  • 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