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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
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
Citation:
S. Bautista, C. A. Morales, “Existence of periodic orbits for singular-hyperbolic sets”, Mosc. Math. J., 6:2 (2006), 265–297
Linking options:
https://www.mathnet.ru/eng/mmj246 https://www.mathnet.ru/eng/mmj/v6/i2/p265
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