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 
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/
@article{TM_2002_236_a10,
     author = {V. S. Gonchenko},
     title = {On {Bifurcations} of {Two-Dimensional} {Diffeomorphisms} with {a~Homoclinic} {Tangency} of {Manifolds} of},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {95--102},
     year = {2002},
     volume = {236},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2002_236_a10/}
}
TY  - JOUR
AU  - V. S. Gonchenko
TI  - On Bifurcations of Two-Dimensional Diffeomorphisms with a Homoclinic Tangency of Manifolds of
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2002
SP  - 95
EP  - 102
VL  - 236
UR  - http://geodesic.mathdoc.fr/item/TM_2002_236_a10/
LA  - ru
ID  - TM_2002_236_a10
ER  - 
%0 Journal Article
%A V. S. Gonchenko
%T On Bifurcations of Two-Dimensional Diffeomorphisms with a Homoclinic Tangency of Manifolds of
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2002
%P 95-102
%V 236
%U http://geodesic.mathdoc.fr/item/TM_2002_236_a10/
%G ru
%F TM_2002_236_a10

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

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.

[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