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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.21 no.1 Antofagasta May 2002

http://dx.doi.org/10.4067/S0716-09172002000100001 

Proyecciones
Vol. 21, N o 1, pp. 1-7, May 2002.
Universidad Católica del Norte
Antofagasta - Chile

PARABOLIC PERTURBATION IN
THE FAMILY

 

JUAN BOBENRIETH ¤
Universidad de Bío - Bío - Chile

 

Abstract

Consider the family of rational maps and the hyperboliccomponent A1 = f w : fw has an attracting fixed point g : We prove that iparabolic parameter with corre-sponding multiplier a primitive there exists a hyperbolic component Wq; attached to A1 at the point w0; which contains w ¡ values for which fw has an at-tracting periodic cycle of period q. 1991 Mathematics Subject Classification : Primary 30D05, 58F23.

 

References

[1] R. Bamon and J.Bobenrieth, ‘The rational maps z 7! 1 + 1=wz d have no Herman rings’, Proceedings of the American Math-ematical Society, (2) 127, pp. 633-636, (1999).        [ Links ]

[2] H. Jellouli, ‘Indice holomorphe et multiplicateur’, The Mandel-brot set, theme and variations (ed Tan Lei), London Mathemati-cal Society Lecture Note Series 274 (Cambridge University Press, 2000), pp. 253-264.        [ Links ]

[3] M. Lyubich, ‘The dynamics of rational transforms : the topolog-ical picture’, Russian Math. Surveys, (4) 41, pp. 43-117, (1986).         [ Links ]

[4] J. Milnor, ‘Geometry and dynamics of quadratic rational maps’, Experimental Mathematics, (1) 2 , pp. 37-83, (1993).        [ Links ]

Received : June 2001.

Juan Bobenrieth
Departamento de Matemáticas
Facultad de Ciencias
Universidad del Bío-Bío
Casilla 5-C
Concepción
Chile
e-mail : jbobenri@ubiobio.cl


¤Partially supported by Fondecyt, Project 1990534

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