SINGULAR CYCLES AND Ck-ROBUST TRANSITIVE SET ON MANIFOLD WITH BOUNDARY
2011 ◽
Vol 13
(02)
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pp. 191-211
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Keyword(s):
Let M be a 3-manifold with boundary ∂M. Let X be a C∞, vector field on M, tangent to ∂M, exhibiting a singular cycle associated to a hyperbolic equilibrium σ∈∂M with real eigenvalues λss < λs < 0 < λu satisfying λs - λss - 2λu > 0. We prove under generic conditions and k large enough the existence of a Ck robust transitive set of X, that is, any Ck vector field Ck close to X exhibits a transitive set containing the cycle. In particular, C∞ vector fields exhibiting Ck robust transitive sets, for k large enough, which are not singular-hyperbolic do exist on any compact 3-manifold with boundary.
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2015 ◽
Vol 08
(02)
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pp. 1550026
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Keyword(s):
2019 ◽
Vol 16
(11)
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pp. 1950180
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1991 ◽
Vol 11
(3)
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pp. 443-454
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1995 ◽
Vol 05
(03)
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pp. 895-899
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Keyword(s):
2021 ◽
Vol 62
◽
pp. 53-66
2015 ◽
Vol 12
(10)
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pp. 1550111
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Keyword(s):
2018 ◽
Vol 148
(4)
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pp. 773-818
Keyword(s):
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