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Confluence of turning points in exact WKB analysis. (English) Zbl 0857.34057

Braaksma, B. L. J. (ed.) et al., The Stokes phenomenon and Hilbert’s 16th problem. Proceedings of the workshop, Groningen, The Netherlands, May 31-June 3, 1995. Singapore: World Scientific. 215-235 (1996).
Summary: This written contribution to the Groningen “Stokes workshop” is different from the talk I delivered there, whose content will be published elsewhere. It deals with a question which was posed to me by A. Its during that talk. The answer I was able to give him at that time only dealt with double turning points. The ideas for coping with turning points of higher multiplicity occurred to me in Cambridge a few weeks later, during my stay in the Newton Institute for the “exponential asymptotics” semester. They were triggered by discussions with F. Olver and O. Daalhuis. I also thank E. Delabaere and V. Kostov for their help in the process of putting these ideas in shape.
For the entire collection see [Zbl 0846.00026].

MSC:

34E20 Singular perturbations, turning point theory, WKB methods for ordinary differential equations
34M60 Singular perturbation problems for ordinary differential equations in the complex domain (complex WKB, turning points, steepest descent)
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