Geodesic
On a~new type of bifurcations on manifolds
Sbornik. Mathematics, Tome 41 (1982) no. 3, pp. 403-407

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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. 
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     author = {V. S. Medvedev},
     title = {On a~new type of bifurcations on manifolds},
     journal = {Sbornik. Mathematics},
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     number = {3},
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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/