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Moscow Mathematical Journal, 2006, Volume 6, Number 2, Pages 265–297
DOI: https://doi.org/10.17323/1609-4514-2006-6-2-265-297 (Mi mmj246) 		 
This article is cited in 28 scientific papers (total in 28 papers)

Existence of periodic orbits for singular-hyperbolic sets

S. Bautistaa, C. A. Moralesb

a Universidad Nacional de Colombia
b Instituto de Matemática, Universidade Federal do Rio de Janeiro
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DOI: https://doi.org/10.17323/1609-4514-2006-6-2-265-297
Abstract: It is well known that on every compact 3-manifold there is a $C^1$ flow displaying a singular-hyperbolic isolated set which has no periodic orbits. By contrast, in this paper we prove that every singular-hyperbolic attracting set of a $C^1$ flow on a compact 3-manifold has a periodic orbit.
Key words and phrases: Singular-hyperbolic set, attracting set, periodic orbit.
Received: March 18, 2005; in revised form January 9, 2006
Bibliographic databases:
MSC: Primary 37D30; Secondary 37D45
Language: English
Citation: S. Bautista, C. A. Morales, “Existence of periodic orbits for singular-hyperbolic sets”, Mosc. Math. J., 6:2 (2006), 265–297
Citation in format AMSBIB
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\by S.~Bautista, C.~A.~Morales
\paper Existence of periodic orbits for singular-hyperbolic sets
\jour Mosc. Math.~J.
\yr 2006
\vol 6
\issue 2
\pages 265--297
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\crossref{https://doi.org/10.17323/1609-4514-2006-6-2-265-297}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2270614}
\zmath{https://zbmath.org/?q=an:1124.37021}
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