On the set where the iterates of an entire function are bounded

2010/12/06 by Walter Bergweiler · 9 citations
Mathematics · #Analytic and geometric function theory #Bounded function #Entire function #Function (biology) #Hausdorff distance #Hausdorff space #Iterated function #Mathematical Dynamics and Fractals #Meromorphic and Entire Functions #Orbit (dynamics) #Set (abstract data type) #math.CV #math.DS #msc:30D05 #msc:37F10 #msc:37F35

paper · pdf · doi:10.1090/s0002-9939-2011-11456-4

published in Proceedings of the American Mathematical Society 140(3), 847-853 (American Mathematical Society) · 7 pages

arxiv created 2010/12/06 · openalex publication_date 2011/11/03 · arxiv updated 2012/02/14 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We show that for a transcendental entire function the set of points whose orbit under iteration is bounded can have arbitrarily small positive Hausdorff dimension.

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