Konstantin Trifonov

pr. Gagarina 23, 603950 Nizhny Novgorod, Russia
Lobachevsky State University of Nizhny Novgorod


Kulagin N. E., Lerman L. M., Trifonov K. N.
Twin Heteroclinic Connections of Reversible Systems
2024, vol. 29, no. 1, pp.  40-64
We examine smooth four-dimensional vector fields reversible under some smooth involution $L$ that has a smooth two-dimensional submanifold of fixed points. Our main interest here is in the orbit structure of such a system near two types of heteroclinic connections involving saddle-foci and heteroclinic orbits connecting them. In both cases we found families of symmetric periodic orbits, multi-round heteroclinic connections and countable families of homoclinic orbits of saddle-foci. All this suggests that the orbit structure near such connections is very complicated. A non-variational version of the stationary Swift – Hohenberg equation is considered, as an example, where such structure has been found numerically.
Keywords: reversible, saddle-focus, heteroclinic, connection, periodic, multi-round
Citation: Kulagin N. E., Lerman L. M., Trifonov K. N.,  Twin Heteroclinic Connections of Reversible Systems, Regular and Chaotic Dynamics, 2024, vol. 29, no. 1, pp. 40-64

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