On mixed dynamics of two-dimensional reversible diffeomorphisms with symmetric non-transversal heteroclinic cycles. (English. Russian original) Zbl 1443.37022
Izv. Math. 84, No. 1, 23-51 (2020); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 84, No. 1, 27-59 (2020).
Summary: We consider one-parameter families (general unfoldings) of two-dimensional reversible diffeomorphisms that contain a diffeomorphism with a symmetric non-transversal heteroclinic cycle. We show that in such families there exist Newhouse intervals of parameters such that the values corresponding to the co-existence of infinitely many stable, completely unstable, saddle and symmetric elliptic periodic orbits are generic (that is, they form Baire second-category sets). Also, the closures of the sets of orbits of different types have non-empty intersections.
MSC:
| 37C05 | Dynamical systems involving smooth mappings and diffeomorphisms |
| 37C29 | Homoclinic and heteroclinic orbits for dynamical systems |
| 37C27 | Periodic orbits of vector fields and flows |
| 37C55 | Periodic and quasi-periodic flows and diffeomorphisms |
Keywords:
heteroclinic cycle; reversible diffeomorphism; homoclinic tangency; bifurcation; periodic orbit; mixed dynamicsReferences:
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