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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap96-1-2,
author = {Maciej Klimek and Marta Kosek},
title = {Generalized iterated function systems, multifunctions and Cantor sets},
journal = {Annales Polonici Mathematici},
volume = {95},
year = {2009},
pages = {25-41},
zbl = {1173.32301},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap96-1-2}
}
Maciej Klimek; Marta Kosek. Generalized iterated function systems, multifunctions and Cantor sets. Annales Polonici Mathematici, Tome 95 (2009) pp. 25-41. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap96-1-2/