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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 $ {\bf 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 $ {\bf 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.
Email: gsl@dimnamica1.fciencias.unam.mx

DOI: https://doi.org/10.1090/S1088-4173-2014-00258-6
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.

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