Asymptotics of relaxation oscilations
Sbornik. Mathematics, Tome 65 (1990) no. 1, pp. 1-17 Cet article a éte moissonné depuis la source Math-Net.Ru

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A complete asymptotics of relaxation oscillations in $R^n$ is constructed. The process is divided into two steps: the construction of the asymptotics of the integral manifold of the system under consideration and the asymptotic integration of the equation in this manifold, with regular dependence on the small parameter. Together with the previously solved stability problem this completes the study of all the main questions connected with the asymptotics of a multidimensional relaxation cycle. Bibliography: 8 titles.
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A. Yu. Kolesov; E. F. Mishchenko. Asymptotics of relaxation oscilations. Sbornik. Mathematics, Tome 65 (1990) no. 1, pp. 1-17. http://geodesic.mathdoc.fr/item/SM_1990_65_1_a0/

[1] Mischenko E. F., Rozov N. Kh., Differentsialnye uravneniya s malym parametrom i relaksatsionnye kolebaniya, Nauka, M., 1975 | MR | Zbl

[2] Rozov N. Kh., “Asimptoticheskoe vychislenie blizkikh k razryvnym periodicheskikh reshenii sistem differentsialnykh uravnenii vtorogo poryadka”, DAN SSSR, 145:1 (1962), 38–40 | MR | Zbl

[3] Mischenko E. F., Pontryagin L. S., “Periodicheskie resheniya sistem differentsialnykh uravnenii, blizkikh k razryvnym”, DAN SSSR, 102:5 (1955), 889–891 | MR | Zbl

[4] Kolesov A. Yu., Kolesov Yu. S, Mischenko E. F., Rozov N. Kh., “Relaksatsionnaya sistema v okrestnosti tochki sryva: svedenie k regulyarnomu sluchayu”, UMN, 43:2 (1988), 141–142 | MR | Zbl | Zbl

[5] Bonet C., “Singular perturbation of relaxed periodic orbits”, J. Diff. Equat., 66:3 (1987), 301–339 | DOI | MR | Zbl

[6] Kolesov A. Yu., Kolesov Yu. S, Mischenko E. F., Rozov N. Kh., “Asimptoticheskoe integrirovanie sistemy v variatsiyakh mnogomernogo relaksatsionnogo tsikla. I, II”, Differents. uravneniya, 23:11 (1987), 1881–1889 ; 12, 2036–2047 | MR | Zbl | Zbl | MR | Zbl

[7] Vasileva A. B., Butuzov V. F., Asimptoticheskie razlozheniya reshenii singulyarno vozmuschennykh uravnenii, Nauka, M., 1973 | MR

[8] Mischenko E. F., “Asimptotika relaksatsionnykh kolebanii”, Matem. sb., 107(149) (1978), 533–540 | MR | Zbl