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Iteration of Analytic Multifunctions

Published online by Cambridge University Press:  22 January 2016

Maciej Klimek
Maciej Klimek*
Affiliation:
Department of Mathematics, Uppsala University, P.O.Box 480, 751-06 Uppsala, Sweden, maciej.klimek@math.uu.se
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Abstract

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It is shown that iteration of analytic set-valued functions can be used to generate composite Julia sets in CN. Then it is shown that the composite Julia sets generated by a finite family of regular polynomial mappings of degree at least 2 in CN, depend analytically on the generating polynomials, in the sense of the theory of analytic set-valued functions. It is also proved that every pluriregular set can be approximated by composite Julia sets. Finally, iteration of infinitely many polynomial mappings is used to give examples of pluriregular sets which are not composite Julia sets and on which Markov’s inequality fails.

Keywords

32F0532H5030D0558F23
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 162 , June 2001 , pp. 19 - 40
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2001

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