[Back]

P. Szmolyan:
"Geometric singular perturbation analysis of turning point problems";
Talk: Vortrag an Universität Oldenburg, Oldenburg (invited); 2021-12-16.

Turning point problems for systems of linear differential equations
εx' = A(t, ε)x with t ∈ R or t ∈ C depending singularly on a small parameter ε are classical difficult problems in asymptotic analysis. Loosely speaking turning points may be characterized as points t_0 at which approximations by natural asymptotic expansions break down. A famous example is the analysis of the eigenvalue problem for the one-dimensional Schrödinger equation based on WKB-methods. In this talk we outline a novel approach to such problems based on geometric singular perturbation theory and the blow-up method.