Stokes Matrices of a Reducible Double Confluent Heun Equation via Monodromy Matrices of a Reducible General Huen Equation with Symmetric Finite Singularities.

We study the effect of the unfolding of a reducible double confluent Heun equation from the point of view of the Stokes phenomenon. We introduce a small complex parameter ε that splits together the non-resonant singular points x = 0 and x = ∞ into four different Fuchsian singularities x L = − ε , x R = ε , and x L L = − 1 / ε , x R R = 1 / ε , respectively. The perturbed equation is a symmetric general Heun equation and its general solution depends analytically on ε . Then we prove that when the perturbed equation has exactly two resonant singularities of different type, all the Stokes matrices of the initial double confluent Heun equation are realized as a limit of the upper-triangular parts of the monodromy matrices of the perturbed equation when ε → 0 . To establish this result we combine a direct computation with a theoretical approach. [ABSTRACT FROM AUTHOR]