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Article

On 4-dimensional flows with wildly embedded invariant manifolds of a periodic orbit

Applied Mathematics and Nonlinear Science. 2020.

 In the present paper we construct an example of 4-dimensional flows on $S^3\times S^1$ whose saddle periodic orbit has a wildly embedded 2-dimensional unstable manifold. We prove that such a property has every suspension under a non-trivial Pixton's diffeomorphism. Moreover we give a complete topological classification of these suspensions.