Geodesic
On mixed dynamics of~two-dimensional reversible diffeomorphisms with symmetric non-transversal heteroclinic cycles
Izvestiya. Mathematics , Tome 84 (2020) no. 1, pp. 23-51

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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.
Keywords: heteroclinic cycle, reversible diffeomorphism, homoclinic tangency, periodic orbit, mixed dynamics.
Mots-clés : bifurcation 
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     title = {On mixed dynamics of~two-dimensional reversible diffeomorphisms with symmetric non-transversal heteroclinic cycles},
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     url = {http://geodesic.mathdoc.fr/item/IM2_2020_84_1_a2/}
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S. V. Gonchenko; M. S. Gonchenko; I. O. Sinitsky. On mixed dynamics of~two-dimensional reversible diffeomorphisms with symmetric non-transversal heteroclinic cycles. Izvestiya. Mathematics , Tome 84 (2020) no. 1, pp. 23-51. http://geodesic.mathdoc.fr/item/IM2_2020_84_1_a2/