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

In the present paper we construct an example of 4-dimensional flows on S × S 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...

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Bibliographic Details
Published in:Applied mathematics and nonlinear sciences 2020-07, Vol.5 (2), p.261-266
Main Authors: Pochinka, Olga V., Shubin, Danila D.
Format: Article
Language:English
Subjects:
37C15
classification
Pixton diffeomorphism
Suspension
wild embedding
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Summary:In the present paper we construct an example of 4-dimensional flows on S × S 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.
ISSN:2444-8656
2444-8656
DOI:10.2478/amns.2020.2.00049