On 4-dimensional flows with wildly embedded invariant manifolds of a periodic orbit
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Nov 13, 2020
About this article
Published Online: Nov 13, 2020
Page range: 261 - 266
Received: Dec 24, 2019
Accepted: Mar 25, 2020
DOI: https://doi.org/10.2478/amns.2020.2.00049
Keywords
© 2020 Olga V. Pochinka et al., published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 International License.
In the present paper we construct an example of 4-dimensional flows on 𝕊3 × 𝕊1 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.