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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Huybrechts, Daniel / Hwang, Jun-Muk / Williamson, Geordie

IMPACT FACTOR 2018: 1.859

CiteScore 2018: 1.14

SCImago Journal Rank (SJR) 2018: 2.554
Source Normalized Impact per Paper (SNIP) 2018: 1.411

Mathematical Citation Quotient (MCQ) 2018: 1.55

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Volume 2008, Issue 624


Siegel disks and periodic rays of entire functions

Lasse Rempe
Published Online: 2008-10-29 | DOI: https://doi.org/10.1515/CRELLE.2008.081


Let f be an entire function whose set of singular values is bounded and suppose that f has a Siegel disk U such that f|U is a homeomorphism. We show that U is bounded. Using a result of Herman, we deduce that if additionally the rotation number of U is Diophantine, then ∂U contains a critical point of f.

Suppose furthermore that all singular values of f lie in the Julia set. We prove that, if f has a Siegel disk U whose boundary contains no singular values, then the condition that f : ∂U → ∂U is a homeomorphism is automatically satisfied. We also investigate landing properties of periodic dynamic rays by similar methods.

About the article

Received: 2004-11-01

Revised: 2007-07-26

Published Online: 2008-10-29

Published in Print: 2008-11-01

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2008, Issue 624, Pages 81–102, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/CRELLE.2008.081.

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