Existence of Infinitely Many Elliptic Periodic Orbits in Four-Dimensional Symplectic Maps with a~Homoclinic Tangency

S. V. Gonchenko ; D. V. Turaev ; L. P. Shilnikov

Informatics and Automation, Dynamical systems and related problems of geometry, Tome 244 (2004), pp. 115-142.

Résumé

We study the problem of coexistence of a countable number of periodic orbits of different topological types (saddles, saddle–centers, and elliptic) in the case of four-dimensional symplectic diffeomorphisms with a homoclinic trajectory to a saddle–focus fixed point.

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