Abstract:
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.
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\Bibitem{Med80}
\by V.~S.~Medvedev
\paper On a~new type of bifurcations on manifolds
\jour Math. USSR-Sb.
\yr 1982
\vol 41
\issue 3
\pages 403--407
\mathnet{http://mi.mathnet.ru/eng/sm2814}
\crossref{https://doi.org/10.1070/SM1982v041n03ABEH002239}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=601891}
\zmath{https://zbmath.org/?q=an:0484.58025|0468.58014}
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https://www.mathnet.ru/eng/sm2814
https://doi.org/10.1070/SM1982v041n03ABEH002239
https://www.mathnet.ru/eng/sm/v155/i3/p487
This publication is cited in the following 12 articles:
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Shilnikov L., Turaev D., “Simple Bifurcations Leading to Hyperbolic Attractors”, Comput. Math. Appl., 34:2-4 (1997), 173–193
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