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Bounded-type Siegel disks of a one-dimensional family of entire functions

Published online by Cambridge University Press:  01 February 2009

LINDA KEEN  and
GAOFEI ZHANG
LINDA KEEN
Affiliation:
Department of Mathematics, Lehman College and Graduate Center, CUNY, Bronx, NY 10468, New York, USA (email: Linda.keen@lehman.cuny.edu)
GAOFEI ZHANG
Affiliation:
Department of Mathematics, Nanjing University, Nanjing, 210093, PR China (email: zhanggf@hotmail.com)
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Abstract

Let 0<θ<1 be an irrational number of bounded type. We prove that for any map in the family (e2πiθz+αz2)ez, α∈ℂ, the boundary of the Siegel disk, with fixed point at the origin, is a quasi-circle passing through one or both of the critical points.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 29 , Issue 1 , February 2009 , pp. 137 - 164
Copyright
Copyright © 2008 Cambridge University Press

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