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Izv. RAN. Ser. Mat., 2017, Volume 81, Issue 4, Pages 108–157 (Mi izv8547)  

Many-circuit canard trajectories and their applications

S. D. Glyzinab, A. Yu. Kolesova, N. Kh. Rozovc

a P.G. Demidov Yaroslavl State University
b Scientific Center in Chernogolovka RAS
c Lomonosov Moscow State University

Abstract: We study the case when two distinct curves of slow motion in a two-dimensional relaxation system with cylindrical phase space intersect each other in a generic way. We establish that the so-called canard trajectories can arise in this situation. They differ from ordinary canard trajectories in the following respect. The passage from the stable curve of slow motion to the unstable one is performed via finitely many asymptotically quick rotations of the phase point around the axis of the cylinder. The results obtained are used in the asymptotic analysis of eigenvalues of a boundary-value problem of Sturm–Liouville type for a singularly perturbed linear Schrödinger equation.

Keywords: singularly perturbed equation, many-circuit canard trajectories, asymptotics, boundary-value problems of Sturm–Liouville type.

Funding Agency Grant Number
Russian Science Foundation 14-21-00158
Russian Foundation for Basic Research 15-01-04066а
This paper was written with the support of the Russian Science Foundation (project no. 14-21-00158) and RFBR, grant no. 15-01-04066a.


DOI: https://doi.org/10.4213/im8547

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English version:
Izvestiya: Mathematics, 2017, 81:4, 771–817

Bibliographic databases:

UDC: 517.926
MSC: 34C26, 34E17, 34E20, 37G99
Received: 14.03.2016

Citation: S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “Many-circuit canard trajectories and their applications”, Izv. RAN. Ser. Mat., 81:4 (2017), 108–157; Izv. Math., 81:4 (2017), 771–817

Citation in format AMSBIB
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