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Conformal Geometry and Dynamics

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Totally disconnected Julia set for different classes of meromorphic functions


Authors: P. Domínguez, A. Hernández and G. Sienra
Journal: Conform. Geom. Dyn. 18 (2014), 1-7
MSC (2010): Primary 37F10; Secondary 30D05.
DOI: https://doi.org/10.1090/S1088-4173-2014-00258-6
Published electronically: January 24, 2014
MathSciNet review: 3157720
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Abstract | References | Similar Articles | Additional Information

Abstract: We study a class of functions $\textbf {A}$ given by Epstein in Towers of finite type complex analytic maps, ProQuest LLC, Ann Arbor, MI, 1993, called finite-type maps. We extend a result related with the Julia set given by Baker, Domínguez in Some connectedness properties of Julia sets, Complex Variable Theory Appl. 41 (2000), 371–389, and Baker, Domínguez, and Herring in Dynamics of functions meromorphic outside a small set, Ergodic Theory Dynam. Systems 21 (2001), 647–672, to functions in class $\textbf {A}$.


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Additional Information

P. Domínguez
Affiliation: F.C. Físico-Matemáticas, Benemérita Universidad Autónoma de Puebla; Av. San Claudio, Col. San Manuel, C.U., Puebla Pue., 72570, México
Email: pdsoto@fcfm.buap.mx

A. Hernández
Affiliation: F.C. Físico-Matemáticas, Benemérita Universidad Autónoma de Puebla; Av. San Claudio, Col. San Manuel, C.U., Puebla Pue., 72570, México
Email: hralberto@hotmail.com

G. Sienra
Affiliation: Facultad de Ciencias, UNAM. Av. Universidad 3000, C.U. México, D.F., 04510, México.
MR Author ID: 223466
Email: gsl@dimnamica1.fciencias.unam.mx

Received by editor(s): September 24, 2012
Published electronically: January 24, 2014
Additional Notes: The authors were supported by CONACYT projects numbers 128005 and 153850
Dedicated: In Memory of I. N. Baker
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.