Trajectories of a quadratic differential related to a quasi-exactly solvable sextic oscillator

Abstract

In this paper, we discuss the existence of solution (as Cauchy transform of a signed measure) of a particular algebraic quadratic equation of the form ${\mathcal{C}}^2\left(z\right)+r\left(z\right)\mathcal{C}\left(z\right)+s\left(z\right)=0.$ This problem remains to describe the critical graph of a related polynomial quadratic differential; in particular, we discuss the existence of finite critical trajectories of this quadratic differential.

20 pages,11 figures. arXiv admin note: text overlap with arXiv:1712.06133

References in corpus (1)

• On spectral polynomials of the Heun equation. II