An example of bifurcation to homoclinic orbits

Journal of Differential Equations - Tập 37 - Trang 351-373 - 1980
Shui-Nee Chow1
1Department of Mathematics, Michigan State University, East Laming, Michigan 48823 U.S.A.

Tài liệu tham khảo

Conley, 1975, Hyperbolic sets and shift automorphisms, 541 Hale, 1978, Interaction of damping and forcing in a second order equation, J. Nonlinear Analysis, 2, 77, 10.1016/0362-546X(78)90043-3 J. K. Hale, Bifurcation near families of solutions, in Proc. Uppsala 1977 International Conference on Differential Equations, published as “Differential Equations,” Acta Universitatis Upsaliensis, Berg, Essen, and Pleijel, Eds. pp. 91–100, Distributed by Almquist and Wiksell, Stockholm. Hale, 1969 Holmes, 1979, Qualitative techniques for bifurcation analysis of complex systems, 608 McGehee, 1974, Homoclinic points of area preserving diffeomorphisms, Amer. J. Math., 96, 409, 10.2307/2373550 Mel'nikov, 1963, On the stability of the center for time periodic solutions, Trans. Moscow Math. Soc., 12, 3 Morozov, 1976, On the complete qualitative investigation of the equation of Duffing, Differentialniye Uravneniya, 12, 241 Newhouse, 1974, Diffeomorphisms with infinitely many sinks, Topology, 13, 9, 10.1016/0040-9383(74)90034-2 Newhouse, 1976, Cycles and bifurcation theory, Asterique, 31, 43 Nitecki, 1971 Smale, 1967, Differentiable dynamical systems, Bull. Amer. Math. Soc., 73, 747, 10.1090/S0002-9904-1967-11798-1