Analytic families of holomorphic iterated function systems

Details Analytic families of holomorphic iterated function systems Analytic families of holomorphic iterated function systems

2008-06-11

arxiv.org/abs/0806.1779v4

Mathematics

Dynamical Systems

30 pages, the title is changed. Published in Nonlinearity 21 (2008) 2255-2279

Scientific paper

10.1088/0951-7715/21/10/004

This paper deals with analytic families of holomorphic iterated function systems. Using real analyticity of the pressure function (which we prove), we establish a classification theorem for analytic families of holomorphic iterated function systems which depend continuously on a parameter when the space of holomorphic iterated function systems is endowed with the "$\lambda$-topology". This classification theorem allows us to generalize some geometric results from the paper ("Lambda-Topology vs. Pointwise Topology", to appear in Ergod. Th. & Dynam. Sys.) of the authors, and gives us a better and clearer understanding of the global structure of the space of conformal IFSs.

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