<abstract xmlns="http://www.w3.org/1999/xhtml">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.</abstract>

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.

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

Applied Mathematics and Nonlinear Sciences

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...

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

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
Suspension, classification, Pixton diffeomorphism, wild embedding

© 2020 Olga V. Pochinka et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

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

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

KeywordsSuspension, classification, Pixton diffeomorphism, wild embedding

© 2020 Olga V. Pochinka et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
Suspension, classification, Pixton diffeomorphism, wild embedding