Abstract
Bifurcations of single-round periodic orbits of three-dimensional diffeomorphisms with a quadratic homoclinic tangency of manifolds of a saddle fixed point with saddle value equal to 1 are studied. Bibliography: 8 titles.
This is a preview of subscription content, log in via an institution to check access.
We’re sorry, something doesn't seem to be working properly.
Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.
REFERENCES
S. V. Gonchenko, D. V. Turaev, and L. P. Shilnikov, “Dynamical phenomena in multi-dimensional systems with a structurally unstable homoclinic Poincare curve,” Dokl. Akad. Nauk, 47, No.3, 410–415 (1993).
N. K. Gavrilov and L. P. Shilnikov, “On three-dimensional dynamical systems close to systems with a structurally unstable homoclinic curve. 1,” Math. Sb. USSR, 17, 467–485 (1972); Part 2, Math. Sb. USSR, 19, 139–156 (1973).
S. V. Gonchenko and L. P. Shilnikov, “Invariants of ω-conjugacy of diffeomorphisms with a structurally unstable homoclinic trajectory,” Ukrainian Math. J., 42, No.2, 134–140 (1990).
S. V. Gonchenko and L. P. Shilnikov, “Moduli of systems with a structurally unstable Poincare homoclinic curve,” Russian Acad. Sci. Izv. Math., 41, No.3, 417–445 (1993).
S. V. Gonchenko, V. S. Gonchenko, and J. C. Tatjer, “Three-dimensional dissipative diffeomorphisms with codimension two homoclinic tangencies and generalized Henon maps,” in: Proceedings of the International Conference “Progress in Nonlinear Science” Dedicated to the 100th Anniversary of A. A. Andronov, Nizhny Novgorod (2001), pp. 63–79.
S. V. Gonchenko and V. S. Gonchenko, “On Andronov-Hopf bifurcations of two-dimensional diffeomorphisms with homoclinic tangencies,” Preprint No. 556, WIAS, Berlin (2000).
S. V. Gonchenko and V. S. Gonchenko, “On bifurcations of birth of close invariant curves in the case of two-dimensional diffeomorphisms with homoclinic tangencies,” Trudy Steklov Math. Inst. (to appear).
V. S. Gonchenko, “On bifurcations of two-dimensional diffeomorphisms with a homoclinic tangency of manifolds of a “neutral” saddle,” Trudy Steklov Math. Inst., 236, 86–93 (2002).
Author information
Authors and Affiliations
Additional information
__________
Published in Zapiski Nauchnykh Seminarov POMI, Vol. 300, 2003, pp. 167-172.
Rights and permissions
About this article
Cite this article
Gonchenko, V.S., Ovsyannikov, I.I. On Bifurcations of Three-Dimensional Diffeomorphisms with a Homoclinic Tangency to a “Neutral” Saddle Fixed Point. J Math Sci 128, 2774–2777 (2005). https://doi.org/10.1007/s10958-005-0229-5
Received:
Issue Date:
DOI: https://doi.org/10.1007/s10958-005-0229-5