Conformal Geometry and Dynamics

Author(s): Linda Keen; Janina Kotus
Journal: Conform. Geom. Dyn. 1 (1997), 28-57.
MSC (1991): Primary 30D05, 58F23, 32H50; Secondary 58F08, 34C35
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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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Retrieve articles in Conformal Geometry and Dynamics with MSC (1991): 30D05, 58F23, 32H50, 58F08, 34C35

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: 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
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
Copyright of article: Copyright 1997, American Mathematical Society

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