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Conformal Geometry and Dynamics

Published by the American Mathematical Society, the Conformal Geometry and Dynamics (ECGD) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4173

The 2020 MCQ for Conformal Geometry and Dynamics is 0.5.

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Unbounded components in parameter space of rational maps
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by Peter M. Makienko PDF
Conform. Geom. Dyn. 4 (2000), 1-21 Request permission

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
  • 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
  • © Copyright 2000 American Mathematical Society
  • Journal: Conform. Geom. Dyn. 4 (2000), 1-21
  • MSC (2000): Primary 37F45; Secondary 37F30
  • DOI: https://doi.org/10.1090/S1088-4173-00-00044-8
  • MathSciNet review: 1741344