The Limit Spectral Graph in the Semi-Classical Approximation for the   Sturm-Liouville Problem With a Complex Polynomial Potential
  The limit distribution of the discrete spectrum of the Sturm-Liouville problem with complex-valued polynomial potential on an interval, on a half-axis, and on the entire axis is studied. It is shown that at large parameter values, the eigenvalues are concentrated along the so-called limit spectral graph; the curves forming this graph are classified. Asymptotics of eigenvalues along curves of various types in the graph are calculated. 
A. A. Shkalikov, S. N. Tumanov
math.SP