Geodesic
On a new type of bifurcations on manifolds
Sbornik. Mathematics, Tome 41 (1982) no. 3, pp. 403-407
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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. 
@article{SM_1982_41_3_a4,
     author = {V. S. Medvedev},
     title = {On a~new type of bifurcations on manifolds},
     journal = {Sbornik. Mathematics},
     pages = {403--407},
     year = {1982},
     volume = {41},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1982_41_3_a4/}
}
TY  - JOUR
AU  - V. S. Medvedev
TI  - On a new type of bifurcations on manifolds
JO  - Sbornik. Mathematics
PY  - 1982
SP  - 403
EP  - 407
VL  - 41
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/SM_1982_41_3_a4/
LA  - en
ID  - SM_1982_41_3_a4
ER  - 
%0 Journal Article
%A V. S. Medvedev
%T On a new type of bifurcations on manifolds
%J Sbornik. Mathematics
%D 1982
%P 403-407
%V 41
%N 3
%U http://geodesic.mathdoc.fr/item/SM_1982_41_3_a4/
%G en
%F SM_1982_41_3_a4
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/

[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