Geodesic
Global bifurcations on a Klein bottle. The general case
Sbornik. Mathematics, Tome 196 (2005) no. 4, pp. 465-483 
A. R. Borisyuk. Global bifurcations on a Klein bottle. The general case. Sbornik. Mathematics, Tome 196 (2005) no. 4, pp. 465-483. http://geodesic.mathdoc.fr/item/SM_2005_196_4_a0/
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     title = {Global bifurcations on a {Klein} bottle. {The} general case},
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     url = {http://geodesic.mathdoc.fr/item/SM_2005_196_4_a0/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

A one-parameter family of smooth vector fields in a space of a high dimension is considered such that for some critical parameter value the corresponding field has a saddle-node cycle (a periodic orbit). The case when the union of the cycle and its homoclinic orbits form a smooth Klein bottle is discussed. The problem consists in the description of the behaviour of the orbit set under the variation of the parameter.

[1] Ilyashenko Yu. S., Li Veigu., Nelokalnye bifurkatsii, MTsNMO CheRo, M., 1999 | MR

[2] Afraimovich V. S., Shilnikov L. P., “O nekotorykh globalnykh bifurkatsiyakh, svyazannykh s ischeznoveniem nepodvizhnoi tochki tipa sedlo-uzel”, Dokl. AN SSSR, 219:3 (1974), 1281–1285

[3] Arnold V. I., Afraimovich V. S., Ilyashenko Yu. S., Shilnikov L. P., “Teoriya bifurkatsii”, Dinamicheskie sistemy, Itogi nauki i tekhniki. Sovr. problemy matem. Fundament. napravleniya, 5, VINITI, M., 1986, 5–218 | MR

[4] Hirsch V. W., Pugh C. C., Shub M., Invariant manifolds, Lecture Notes in Math., 583, Springer-Verlag, New York, 1977 | MR | Zbl

[5] Fenichel N., “Persistence and smoothness of invariant manifolds for flows”, Indiana Univ. Math. J., 21 (1971), 193–226 | DOI | MR | Zbl

[6] Medvedev V. S., “O novom tipe bifurkatsii na mnogoobraziyakh”, Matem. sb., 113 (155):3 (1980), 487–492 | MR | Zbl

[7] Borisyuk A. R., “Globalnye bifurkatsii na butylke Kleina. Unimodalnyi sluchai”, Matem. zametki, 71:3 (2002), 348–363 | MR | Zbl

[8] Arnold V. I., Varchenko A. N., Gusein-Zade S. M., Osobennosti differentsiruemykh otobrazhenii. I, Nauka, M., 1982 | MR