On mixed dynamics of~two-dimensional reversible diffeomorphisms with symmetric non-transversal heteroclinic cycles

S. V. Gonchenko ; M. S. Gonchenko ; I. O. Sinitsky

Izvestiya. Mathematics , Tome 84 (2020) no. 1, pp. 23-51.

Résumé

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.

Détail

Keywords: heteroclinic cycle, reversible diffeomorphism, homoclinic tangency, periodic orbit, mixed dynamics.
Mots-clés : bifurcation

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