On the accumulation of separatrices by invariant circles
Keyword(s):
Abstract Let f be a smooth symplectic diffeomorphism of ${\mathbb R}^2$ admitting a (non-split) separatrix associated to a hyperbolic fixed point. We prove that if f is a perturbation of the time-1 map of a symplectic autonomous vector field, this separatrix is accumulated by a positive measure set of invariant circles. However, we provide examples of smooth symplectic diffeomorphisms with a Lyapunov unstable non-split separatrix that are not accumulated by invariant circles.
1990 ◽
Vol 10
(4)
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pp. 793-821
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2009 ◽
Vol 29
(4)
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pp. 1349-1367
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2020 ◽
Vol 50
(4)
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pp. 442-453
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2009 ◽
Vol 19
(07)
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pp. 2181-2191
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1995 ◽
Vol 15
(6)
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pp. 1045-1059
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