Abstract
AbstractLet 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.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,General Mathematics
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