On the Existence of Finite Critical Trajectories in a Family of Quadratic Differentials

Abstract

In this note, we discuss the possible existence of finite critical trajectories connecting two zeros in a family of quadratic differentials satisfying some properties. We treat the cases of holomorphic and meromorphic quadratic differentials. In addition, we reprove some results about the support of limiting root-counting measures of the generalized Laguerre and Jacobi polynomials with varying parameters.2010 Mathematics subject classification: 30C15, 31A35, 34E05.

Fingerprints of Closed Trajectories of a Strebel Quadratic Differential

“…The local and global structures of the trajectories is well known (more details about the theory of quadratic differentials can be found in [4], [3], or [5]). The set C \ Γ f consists of a finite number of domains called the Configurations Domain of .…”

Lemniscates as Trajectories of Quadratic Differentials (I)

“…The local and global structures of the trajectories is well known (more details about the theory of quadratic differentials can be found in [5], [3], or [6]), in particular :…”