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Conformal Geometry and Dynamics
Conformal Geometry and Dynamics
ISSN 1088-4173

 

Dynamics of the family $\lambda \tan z$


Authors: Linda Keen and Janina Kotus
Journal: Conform. Geom. Dyn. 1 (1997), 28-57
MSC (1991): Primary 30D05, 58F23, 32H50; Secondary 58F08, 34C35
Published electronically: August 13, 1997
MathSciNet review: 1463839
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Abstract: We study the the tangent family ${\mathcal F} = \{\lambda \tan z, \lambda \in {\mathbb C} - \{0\}\}$ and give a complete classification of their stable behavior. We also characterize the the hyperbolic components and give a combinatorial description of their deployment in the parameter plane.


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Additional Information

Linda Keen
Affiliation: Department of Mathematics, CUNY Lehman College, Bronx, New York 10468
Email: linda@alpha.lehman.cuny.edu

Janina Kotus
Affiliation: Institute of Mathematics, Technical University of Warsaw, 00-661 Warsaw, Poland
Email: janinak@snowman.impan.gov.pl

DOI: http://dx.doi.org/10.1090/S1088-4173-97-00017-9
PII: S 1088-4173(97)00017-9
Keywords: Iteration, meromorphic function, tangent, holomorphic motion, Julia set, parameter plane
Received by editor(s): April 28, 1997
Published electronically: August 13, 1997
Additional Notes: The first author was supported in part by NSF Grant DMS-9205433, PSC-CUNY Award, I.B.M. and M.S.R.I
The second author was supported in part by Polish KBN Grant No 21046910 “Iteracje i fraktale” and KBN Grant No 2 P03A 025 12 “Iteracje funkcji holomorficznych", the Fulbright Foundation, I.M.S. Stony Brook and M.S.R.I
Article copyright: © Copyright 1997 American Mathematical Society