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Conformal Geometry and Dynamics

ISSN 1088-4173

 

 

Unbounded components in parameter space of rational maps


Author: Peter M. Makienko
Journal: Conform. Geom. Dyn. 4 (2000), 1-21
MSC (2000): Primary 37F45; Secondary 37F30
Published electronically: February 23, 2000
MathSciNet review: 1741344
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Abstract:

Using pinching deformations of Riemann surfaces, we give several sufficient criteria for the space of quasiconformal deformations of rational map $R$ of degree $d$ to have non-compact closure in the space $Rat_{d}$ of rational maps of degree $d$ modulo conjugation by Möbius transformations.


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Additional Information

Peter M. Makienko
Affiliation: Institute for Applied Mathematics, Shevchenko str. 9, Khabarovsk, 680 000, Russia
Address at time of publication: Instituto de Matematicas Unidad Cuernavaca, Universidad Nacional Autonoma de Mexico, A.P. 273-3 Admon. de Correos #3, 62251 Cuernavaca, Morelos, Mexico
Email: makienko@iam.khv.ru, makienko@matcuer.unam.mx

DOI: https://doi.org/10.1090/S1088-4173-00-00044-8
Received by editor(s): December 27, 1998
Received by editor(s) in revised form: September 14, 1999
Published electronically: February 23, 2000
Additional Notes: This work has been partially supported by the Russian Fund of Basic Researches, Grant 99-01-01006
Article copyright: © Copyright 2000 American Mathematical Society