Rigidity of Conformal Iterated Function Systems

@inproceedings{Mauldin1999RigidityOC,
  title={Rigidity of Conformal Iterated Function Systems},
  author={Daniel Mauldin and Feliks Przytycki},
  year={1999}
}
The paper extends the rigidity of mixing expanding repellers theorem by D. Sullivan announced at 1986 IMC Su], see also the unpublished manuscript by the second author Pr]. We show that for a regular conformal, satisfying "Open Set Condition", iterated function system of countably many holomorphic contractions of an open connected subset of a complex plane, the Radon-Nikodym derivative dd=dm has a real-analytic extension on an open neighbourhood of the limit set of this system, where m is the… CONTINUE READING
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