It is proved that in the space of -smooth () flows in () there exist regions filled by systems that each have an attractor (here: a completely stable chain-transitive closed invariant set) containing a non-trivial basic hyperbolic set together with its unstable manifold, which has points of non-transversal intersection with the stable manifold. A construction is given for such a wild attractor containing an equilibrium state of saddle-focus type.
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Turaev et al. (1998) studied this question.
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