On the existence of finite critical trajectories in a family of quadratic differentials

In this note, we discuss the possible existence of finite critical trajectories connecting two zeros a(t) and b(t) of a family of quadratic differentials satisfying some properties. We treat the cases of holomorphic and meromorphic quadratic differentials, and we give new proofs concerning the suppo...

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Bibliographic Details
Published in:arXiv.org 2015-12
Main Author: Thabet, Faouzi
Format: Article
Language:English
Subjects:
Polynomials
Trajectories
Online Access:Get full text
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Summary:In this note, we discuss the possible existence of finite critical trajectories connecting two zeros a(t) and b(t) of a family of quadratic differentials satisfying some properties. We treat the cases of holomorphic and meromorphic quadratic differentials, and we give new proofs concerning the supports of limit measures of the root-counting measures of the generalized Laguerre and Jacobi polynomials with varying parameters.
ISSN:2331-8422
DOI:10.48550/arxiv.1509.04965