Geodesic
On bifurcations of three-dimensional diffeomorphisms with a homoclinic tangency to a “neutral” saddle fixed point
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems. Part VIII, Tome 300 (2003), pp. 167-172 
V. S. Gonchenko; I. I. Ovsyannikov. On bifurcations of three-dimensional diffeomorphisms with a homoclinic tangency to a “neutral” saddle fixed point. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems. Part VIII, Tome 300 (2003), pp. 167-172. http://geodesic.mathdoc.fr/item/ZNSL_2003_300_a14/
@article{ZNSL_2003_300_a14,
     author = {V. S. Gonchenko and I. I. Ovsyannikov},
     title = {On bifurcations of three-dimensional diffeomorphisms with a~homoclinic tangency to a~{\textquotedblleft}neutral{\textquotedblright} saddle fixed point},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {167--172},
     year = {2003},
     volume = {300},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2003_300_a14/}
}
TY  - JOUR
AU  - V. S. Gonchenko
AU  - I. I. Ovsyannikov
TI  - On bifurcations of three-dimensional diffeomorphisms with a homoclinic tangency to a “neutral” saddle fixed point
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2003
SP  - 167
EP  - 172
VL  - 300
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2003_300_a14/
LA  - en
ID  - ZNSL_2003_300_a14
ER  - 
%0 Journal Article
%A V. S. Gonchenko
%A I. I. Ovsyannikov
%T On bifurcations of three-dimensional diffeomorphisms with a homoclinic tangency to a “neutral” saddle fixed point
%J Zapiski Nauchnykh Seminarov POMI
%D 2003
%P 167-172
%V 300
%U http://geodesic.mathdoc.fr/item/ZNSL_2003_300_a14/
%G en
%F ZNSL_2003_300_a14

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

Bifurcations of single-round periodic orbits of three-dimensional diffeomorphisms with a quadratic homoclinic tangency of manifolds of a saddle fixed point with the saddle value equal to 1 are studied.

[1] S. V. Gonchenko, D. V. Turaev, L. P. Shilnikov, “Dynamical phenomena in multi-dimensional systems with a structurally unstable homoclinic Poincare curve”, Dokl. RAN, 47:3 (1993), 410–415 | MR | Zbl

[2] N. K. Gavrilov, L. P. Shilnikov, “On three-dimensional dynamical systems close to systems with a structurally unstable homoclinic curve, 1”, Math. Sb. USSR, 17 (1972), 467–485 ; “Part 2”, Math. Sb. USSR, 19 (1973), 139–156 | DOI | DOI

[3] S. V. Gonchenko, L. P. Shilnikov, “Invariants of $\Omega$-conjugacy of diffeomorphisms with a structurally unstable homoclinic trajectory”, Ukr. Math. J., 42:2 (1990), 134–140 | DOI | MR | Zbl

[4] S. V. Gonchenko, L. P. Shilnikov, “On the moduli of systems with a non-rough Poincare homoclinic curve”, Russian Acad. Sci. Izv. Math., 41:3 (1993), 417–445 | DOI | MR | Zbl

[5] S. V. Gonchenko, V. S. Gonchenko, J. C. Tatjer, “Three-dimensional dissipative diffeomorphisms with codimension two homoclinic tangencies and generalized Hénon maps”, Progress in Nonlinear Science, Proc. of Int. Conf. dedicated to 100th Anniversary of A. A. Andronov, 2001, 63–79 | MR

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

[7] S. V. Gonchenko, V. S. Gonchenko, “On bifurcations of birth of close invariant curves in the case of two-dimensional diffeomorphisms with homoclinic tangencies”, Proc. of Steklov Math. Inst., in press

[8] V. S. Gonchenko, “On bifurcations of two-dimensional diffeomorphisms with a homoclinic tangency of manifolds of a “neutral” saddle”, Proc. of Steklov Math. Inst., 236, 2002, 86–93 | MR | Zbl