On systems with a saddle-focus homoclinic curve

Mathematics of the USSR - Sbornik

Volumn 58, Issue 2, 1987, Pages 557-574

  Ovsyannikov, I M ^a   Shil'nikov L P ^a  

^a I M SECHENOV FIRST MOSCOW STATE MEDICAL UNIVERSITY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 79955579216     PISSN: 00255734     EISSN: 21695288     Source Type: Journal    
DOI: 10.1070/SM1987v058n02ABEH003120     Document Type: Article

References (9)

1. L. P. Shil'nikov, A case of the existence of a countable number of periodic motions, Dokl. Akad. Nauk SSSR 160(1965), 558-561; English transl. in Soviet Math. Dokl. 6(1965).
2. L. P. Shil'nikov, A contribution to the problem of the structure of an extended neighborhood of a structurally unstable equilibrium state of saddle-focus type, Mat. Sb. 81(123) (1970), 92-103; English transl. in Math. USSR Sb. 10(1970).
3. L. P. Shil'nikov, Bifurcation theory and turbulence, Nonlinear and Turbulent Processes in Physics (Proc. Second Internat. Workshop, Kiev, 1983; R. Z. Sagdeev, editor), Vol. 111, Harwood Academic Publ., Cher, 1984, pp. 1627-1635.
4. Sheldon E. Newhouse, The abundance of wild hyperbolic sets and nonsmooth stable sets for diffeomor-phisms, Inst. Hautes Etudes Sci. Publ. Math. No. 50 (1979), 101-151.
5. L. P. Shil'nikov, Bifurcation theory and the Lorenz model, Appendix to the Russian transl. of J. E. Marsden et al., The Hopf bifurcation and its applications, “Mir”, Moscow, 1980, pp. 317-335. (Russian).
6. N. K. Gavrilov and L. P. Shil'nikov, On three-dimensional dynamical systems close to systems with a structurally unstable homoclinic curve.II, Mat. Sb. 90(132) (1973), 139-156; English transl. in Math. USSR Sb. 19(1973).
7. V. S. Afraimovich, Smooth changes of variables, Methods of the Qualitative Theory of Differential Equations (E. A. Leontovich [-Andronova], editor), Gor'kov. Gos. Univ., Gorki, 1984, pp. 10-21. (Russian).
8. Peter Lancaster, Theory of matrices, Academic Press, 1969.
9. L. P. Shil'nikov, Some cases of generation of periodic motions from singular trajectories, Mat. Sb. 61(103) (1963), 443-466. (Russian).