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 C2( z) +r( z) C( z) +s( z) =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.
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