Geodesic
Solution of the operator equation $i\varepsilon dy/dt=A(t)y$ on intervals containing turning points
Teoretičeskaâ i matematičeskaâ fizika, Tome 122 (2000) no. 3, pp. 357-371 
E. A. Grinina. Solution of the operator equation $i\varepsilon dy/dt=A(t)y$ on intervals containing turning points. Teoretičeskaâ i matematičeskaâ fizika, Tome 122 (2000) no. 3, pp. 357-371. http://geodesic.mathdoc.fr/item/TMF_2000_122_3_a3/
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Voir la notice de l'article provenant de la source Math-Net.Ru

We obtain formal solutions of the equation $i\varepsilon dy/dt=A(t)y$ in the form of complete asymptotic expansions as $\varepsilon\to0$ on intervals containing parabolic or hyperbolic turning points. The highest orders of the power series in $\varepsilon$ for the formal solutions are studied in detail.

[1] V. Buslaev, A. Grigis, Turning points, Preprint No 98-21, Mathemetiques de l'Universite Paris-Nord, 1998

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[3] S. G. Krein, Lineinye differentsialnye uravneniya v banakhovom prostranstve, Nauka, M., 1969 | MR

[4] V. S. Buldyrev, S. Yu. Slavyanov, “Regulyarizatsiya fazovykh integralov vblizi vershiny barera”, Problemy matematicheskoi fiziki. Vyp. 10. Spektralnaya teoriya. Volnovye protsessy, eds. M. Sh. Birman i dr., Izd-vo Leningradskogo universiteta, L., 1982, 50–70 | MR