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A NOTE ON RANDOM HOLOMORPHIC ITERATION IN CONVEX DOMAINS

Published online by Cambridge University Press:  28 July 2008

Filippo Bracci
Filippo Bracci
Affiliation:
Dipartimento di Matematica, Università di Roma ‘Tor Vergata', Via della Ricerca Scientifica 1, 00133 Rome, Italy (fbracci@mat.uniroma2.it)
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Abstract

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We introduce a geometric condition of Bloch type which guarantees that a subset of a bounded convex domain in several complex variables is degenerate with respect to every iterated function system. Furthermore, we discuss the relations of such a Bloch-type condition with the analogous hyperbolic Lipschitz condition.

Keywords

Primary 32H50Secondary 70K99iterated function systemsdegenerate subsetcomplex geodesiciterationconvex domain
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 51 , Issue 2 , June 2008 , pp. 297 - 304
Copyright
Copyright © Edinburgh Mathematical Society 2008