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Conformal Geometry and Dynamics

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Mating a Siegel disk with the Julia set of a real quadratic polynomial

Authors: G. Ble and R. Valdez
Journal: Conform. Geom. Dyn. 10 (2006), 257-284
MSC (2000): Primary 37F10; Secondary 37F45, 37F50
Published electronically: October 5, 2006
MathSciNet review: 2261051
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Abstract: In this work, we show that it is possible to construct the mating between a quadratic polynomial with a Siegel disk and a real quadratic polynomial possessing a postcritical orbit that is semi-conjugate to a rigid rotation with the same rotation number as the Siegel disk.

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Additional Information

G. Ble
Affiliation: División Académica de Ciencias Básicas, Universidad Juárez Autónoma de Tabasco, Km. 1 Carr. Cunduacán-Jalpa, C.P. 86690, Cunduacán, Tabasco, México

R. Valdez
Affiliation: Facultad de Ciencias, Universidad Autónoma del Estado de Morelos, Av. Universidad 1001, col. Lomas de Chamilpa, C.P. 62210 Cuernavaca, Morelos, México

Keywords: Holomorphic dynamics, rational map, mating, Julia set, Mandelbrot set
Received by editor(s): February 10, 2006
Published electronically: October 5, 2006
Additional Notes: The first author was supported by CONACYT, 42249
The second author was supported by PROMEP, UAEMOR-PTC-166
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.