Geodesic
On Bifurcations of Two-Dimensional Diffeomorphisms with a Homoclinic Tangency of Manifolds of
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 236 (2002), pp. 95-102
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Bifurcations of periodic orbits are studied for two-dimensional diffeomorphisms close to a diffeomorphism with the quadratic homoclinic tangency to a saddle fixed point whose Jacobian is equal to one. Problems of the coexistence of periodic orbits of various types of stability are considered. 
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V. S. Gonchenko. On Bifurcations of Two-Dimensional Diffeomorphisms with a Homoclinic Tangency of Manifolds of. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 236 (2002), pp. 95-102. http://geodesic.mathdoc.fr/item/TM_2002_236_a10/

[1] Gavrilov N. K., Shilnikov L. P., “O trekhmernykh dinamicheskikh sistemakh, blizkikh k sisteme s negruboi gomoklinicheskoi krivoi, I, II”, Mat. sb., 88:4 (1972), 475–492 ; 90:1 (1973), 139–157 | MR | Zbl | MR

[2] Gonchenko S. V., Gonchenko V. S., On Andronov–Hopf bifurcations of two-dimensional diffeomorphisms with homoclinic tangencies, Preprint No 556, WIAS, Berlin, 2000 | MR

[3] Gonchenko S. V., Shilnikov L. P., “Invarianty $\Omega$-sopryazhennosti diffeomorfizmov s negruboi gomoklinicheskoi traektoriei”, Ukr. mat. zhurn., 42:2 (1990), 153–159 | MR | Zbl