Generalized iterated function systems, multifunctions and Cantor sets

Volume 96 / 2009

Maciej Klimek, Marta Kosek Annales Polonici Mathematici 96 (2009), 25-41 MSC: Primary 32H02, 32A12, 32H50; Secondary 46G20, 54C50, 26E25. DOI: 10.4064/ap96-1-2


Using a construction similar to an iterated function system, but with functions changing at each step of iteration, we provide a natural example of a continuous one-parameter family of holomorphic functions of infinitely many variables. This family is parametrized by the compact space of positive integer sequences of prescribed growth and hence it can also be viewed as a parametric description of a trivial analytic multifunction.


  • Maciej KlimekDepartment of Mathematics
    Uppsala University
    P.O. Box 480
    751-06 Uppsala, Sweden
  • Marta KosekInstitute of Mathematics
    Jagiellonian University
    /Lojasiewicza 6
    30-348 Kraków, Poland

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