Article
On 4-dimensional flows with wildly embedded invariant manifolds of a periodic orbit
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Abstract
In the present paper we construct an example of 4-dimensional flows on π3 Γ π1 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.
Keywords
Suspension, classification, Pixton diffeomorphism, wild embedding, 37C15
Citation
Pochinka, O. V. & Shubin, D. D. (2020). On 4-dimensional flows with wildly embedded invariant manifolds of a periodic orbit. Applied Mathematics and Nonlinear Sciences, 5(2), 261β266. https://doi.org/10.2478/amns.2020.2.00049
O. V. Pochinka and D. D. Shubin, “On 4-dimensional flows with wildly embedded invariant manifolds of a periodic orbit,” Applied Mathematics and Nonlinear Sciences, vol. 5, no. 2, pp. 261β266, 2020, doi: 10.2478/amns.2020.2.00049.
Pochinka OV, Shubin DD. On 4-dimensional flows with wildly embedded invariant manifolds of a periodic orbit. Applied Mathematics and Nonlinear Sciences. 2020;5(2):261β266. doi:10.2478/amns.2020.2.00049.
Pochinka, O. V. and Shubin, D. D. (2020), ‘On 4-dimensional flows with wildly embedded invariant manifolds of a periodic orbit’, Applied Mathematics and Nonlinear Sciences, 5(2), pp. 261β266. Available at: https://doi.org/10.2478/amns.2020.2.00049.
Pochinka, Olga V., and Danila D. Shubin. “On 4-dimensional Flows with Wildly Embedded Invariant Manifolds of a Periodic Orbit.” Applied Mathematics and Nonlinear Sciences, vol. 5, no. 2, 2020, pp. 261β266. https://doi.org/10.2478/amns.2020.2.00049.
Pochinka, Olga V., and Danila D. Shubin. “On 4-dimensional Flows with Wildly Embedded Invariant Manifolds of a Periodic Orbit.” Applied Mathematics and Nonlinear Sciences 5, no. 2 (2020): 261β266. https://doi.org/10.2478/amns.2020.2.00049.
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Published by: Engineering Journals
