On 4-dimensional flows with wildly embedded invariant manifolds of a periodic orbit
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13. Nov. 2020
Über diesen Artikel
Online veröffentlicht: 13. Nov. 2020
Seitenbereich: 261 - 266
Eingereicht: 24. Dez. 2019
Akzeptiert: 25. März 2020
DOI: https://doi.org/10.2478/amns.2020.2.00049
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© 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.