This is a preview of subscription content, log in via an institution to check access.
Literature cited
L. P. Shil'nikov, “Poincare—Birkhoff problem,” Mat. Sb.,74, No. 1, 378–397 (1967).
N. K. Gavrilov and L. P. Shil'nikov, “Three-dimensional dynamical systems, close to systems with structurally unstable homoclinic curve. I,” Mat. Sb.,88, No. 8, 475–492 (1972); II,90, No. 1, 139–156 (1973).
N. K. Gavrilov, “n-Dimensional dynamical systems, close to systems with structurally unstable homoclinic curve,” Dokl. Akad. Nauk SSSR,212, No. 2, 276–279 (1973).
S. Newhouse, “Diffeomorphisms with infinitely many sinks,” Topology,12, 8–18 (1974).
L. P. Shil'nikov, “Structure of the neighborhood of a homoclinic tube of an invariant torus,” Dokl. Akad. Nauk SSSR,180, No. 2, 286–289 (1968).
L. P. Shil'nikov, “A new type of bifurcation of multidimensional dynamical systems,” Dokl. Akad. Nauk SSSR,189, No. 1, 59–62 (1969).
L. P. Shil'nikov, “Generation of periodic motions from trajectories doubly-asymptotic with an equilibrium state of saddle type,” Mat. Sb.,77, No. 3, 461–472 (1968).
Z. Nitecki, Introduction to Differential Dynamics [Russian translation], Mir, Moscow (1975).
N. Bourbaki, Differentiable and Analytic Varieties (Compendium of Results) [Russian translation], Mir, Moscow (1975).
V. S. Afraimovich and L. P. Shil'nikov, “Singular sets of Morse-Smale systems,” Tr. Mosk. Mat. O-va,28, 181–214 (1973).
Author information
Authors and Affiliations
Additional information
Translated from Matematicheskie Zametki, Vol. 33, No. 5, pp. 745–755, May, 1983.
In conclusion, the author thanks L. P. Shil'nikov for proposing the problem and for constant interest in the work.
Rights and permissions
About this article
Cite this article
Gonchenko, S.V. Stable periodic motions in systems close to a structurally unstable homoclinic curve. Mathematical Notes of the Academy of Sciences of the USSR 33, 384–389 (1983). https://doi.org/10.1007/BF01158287
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01158287