Geodesic
Existence of Infinitely Many Elliptic Periodic Orbits in Four-Dimensional Symplectic Maps with a~Homoclinic Tangency
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Dynamical systems and related problems of geometry, Tome 244 (2004), pp. 115-142

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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. 
@article{TM_2004_244_a6,
     author = {S. V. Gonchenko and D. V. Turaev and L. P. Shilnikov},
     title = {Existence of {Infinitely} {Many} {Elliptic} {Periodic} {Orbits} in {Four-Dimensional} {Symplectic} {Maps} with {a~Homoclinic} {Tangency}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {115--142},
     publisher = {mathdoc},
     volume = {244},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2004_244_a6/}
}
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S. V. Gonchenko; D. V. Turaev; L. P. Shilnikov. Existence of Infinitely Many Elliptic Periodic Orbits in Four-Dimensional Symplectic Maps with a~Homoclinic Tangency. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Dynamical systems and related problems of geometry, Tome 244 (2004), pp. 115-142. http://geodesic.mathdoc.fr/item/TM_2004_244_a6/