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ON THE EXISTENCE OF FINITE CRITICAL TRAJECTORIES IN A FAMILY OF QUADRATIC DIFFERENTIALS

Part of: Geometric function theory Asymptotic theory Two-dimensional theory

Published online by Cambridge University Press:  16 March 2016

FAOUZI THABET
FAOUZI THABET*
Affiliation:
Institut Supérieur des Sciences Appliquées et de Technologie de Gabès, Avenue Omar Ibn El Khattab, 6029, Tunisia email faouzithabet@yahoo.fr
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Abstract

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We discuss the existence of finite critical trajectories connecting two zeros in certain families of quadratic differentials. In addition, we reprove some results about the support of the limiting root-counting measures of the generalised Laguerre and Jacobi polynomials with varying parameters.

Keywords

quadratic differentialstrajectories and orthogonal trajectorieshomotopic classesgeodesicsLaguerre and Jacobi polynomials

MSC classification

Primary: 30C15: Zeros of polynomials, rational functions, and other analytic functions (e.g. zeros of functions with bounded Dirichlet integral)
Secondary: 31A35: Connections with differential equations 34E05: Asymptotic expansions
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 94 , Issue 1 , August 2016 , pp. 80 - 91
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

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