<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

Publicado en línea: 13 nov 2020

Páginas: 261 - 266

Recibido: 24 dic 2019

Aceptado: 25 mar 2020

DOI: https://doi.org/10.2478/amns.2020.2.00049

Palabras clave
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.

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

Publicado en línea: 13 nov 2020

Páginas: 261 - 266

Recibido: 24 dic 2019

Aceptado: 25 mar 2020

DOI: https://doi.org/10.2478/amns.2020.2.00049

Palabras claveSuspension, 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.

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Palabras clave
Suspension, classification, Pixton diffeomorphism, wild embedding