Analytic Multifunctions, Holomorphic Motions and Hausdorff Dimension in IFSs

• Autores: line Baribeau, Mario Roy
• Localización: Monatshefte für mathematik, ISSN 0026-9255, Vol. 147, Nº 3, 2006, págs. 199-217
• Idioma: alemán
• DOI: 10.1007/s00605-005-0365-5
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• Resumen

  • We study iterated function systems of contractions which depend holomorphically on a complex parameter ?. We first restrict our attention to systems which consist of similarities that satisfy the OSC. In this setting, we prove that the Hausdorff dimension of the limit set J(?) is a continuous, subharmonic function of ?. In the remainder of the paper, systems consisting of conformal contractions are considered. We give conditions under which J(?) and A(?) = describe a holomorphic motion, and construct an example that shows that this is not the case in general. We finally show that A(?) is best described as an analytic multifunction of ?, a notion that generalizes that of holomorphic motion