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Siegel disks and periodic rays of entire functions
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Lasse Rempe
Published/Copyright:
October 29, 2008
Abstract
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.
Received: 2004-11-01
Revised: 2007-07-26
Published Online: 2008-10-29
Published in Print: 2008-November
© Walter de Gruyter Berlin · New York 2008
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- The spinorial τ-invariant and 0-dimensional surgery
- Well-posedness, blow-up phenomena, and global solutions for the b-equation
- Siegel disks and periodic rays of entire functions
- Isomorphisms between Leavitt algebras and their matrix rings
- The number of smallest parts in the partitions of n
- Modular analogues of Jordan's theorem for finite linear groups
- Prime specialization in higher genus I
- Filling inequalities do not depend on topology
- Erratum to "Modular curves and Ramanujan's continued fraction"
Articles in the same Issue
- Topology of negatively curved real affine algebraic surfaces
- The spinorial τ-invariant and 0-dimensional surgery
- Well-posedness, blow-up phenomena, and global solutions for the b-equation
- Siegel disks and periodic rays of entire functions
- Isomorphisms between Leavitt algebras and their matrix rings
- The number of smallest parts in the partitions of n
- Modular analogues of Jordan's theorem for finite linear groups
- Prime specialization in higher genus I
- Filling inequalities do not depend on topology
- Erratum to "Modular curves and Ramanujan's continued fraction"
