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Bifurcations of meromorphic vector fields on the Riemann sphere

Published online by Cambridge University Press:  14 October 2010

Jesús Muciño-Raymundo  and
Carlos Valero-Valdés
Jesús Muciño-Raymundo
Affiliation:
Institute de Matemáticas, UNAM, Coyoacán, México 04510 D.F. Mexico
Carlos Valero-Valdés
Affiliation:
Institute de Matemáticas, UNAM, Coyoacán, México 04510 D.F. Mexico
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Abstract

Let {Xθ} be a family of rotated singular real foliations in the Riemann sphere which is the result of the rotation of a meromorphic vector field X with zeros and poles of multiplicity one. We prove that the set of bifurcation values, in the circle {θ}, is for each family a set with at most a finite number of accumulation points. A condition which implies a finite number of bifurcation values is given. We also show that the property of having an infinite set of bifurcation values defines open but not dense sets in the space of meromorphic vector fields with fixed degree.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 15 , Issue 6 , December 1995 , pp. 1211 - 1222
Copyright
Copyright © Cambridge University Press 1995

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