Geodesic
On a new type of bifurcations on manifolds
Sbornik. Mathematics, Tome 41 (1982) no. 3, pp. 403-407 
V. S. Medvedev. On a new type of bifurcations on manifolds. Sbornik. Mathematics, Tome 41 (1982) no. 3, pp. 403-407. http://geodesic.mathdoc.fr/item/SM_1982_41_3_a4/
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     title = {On a~new type of bifurcations on manifolds},
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Voir la notice de l'article provenant de la source Math-Net.Ru

Palis and Pugh asked if there exists a one-parameter family of smooth vector fields on a compact manifold, having a closed orbit which depends continuously on the parameter but whose period is not bounded above (as a function of the parameter) and which disappears at a finite (positive) distance from the set of singular points of the vector field. In this paper we answer this question affirmatively. Moreover, we formulate a condition for the existence of the corresponding bifurcation of a smooth vector field without singularities on a closed two-dimensional manifold, and we give concrete examples. Bibliography: 4 titles.

[1] Dzh. Peilis, Ch. Pyu, Pyatdesyat problem v teorii dinamicheskikh sistem

[2] S. X. Aranson, “Ob otsutstvii nezamknutykh ustoichivykh po Puassonu polutraektorii i traektorii, dvoyakoasimptoticheskikh k dvoinomu predelnomu tsiklu, u dinamicheskikh sistem pervoi stepeni negrubosti na orientiruemykh dvumernykh mnogoobraziyakh”, Matem. sb., 76(118) (1968), 214–230 | MR | Zbl

[3] J. Sotomayer, “Generic one-parameter families of vector fields on two-dimensional manifolds”, Bull. Amer. Math. Soc., 74 (1968), 722–726 | DOI | MR | Zbl

[4] V. S. Afraimovich, L. P. Shilnikov, “O dostizhimykh perekhodakh ot sistem Morsa–Smeila k sistemam so mnogimi periodicheskimi dvizheniyami”, Izv. AN SSSR, seriya matem., 38 (1974), 1248–1288 | Zbl