Using Melnikov's method to solve Silnikov's problems

10.1016/0022-0396(84)90082-2

4 Chow S. N. , Deng B. and Fiedler B. . Homoclinic bifurcations at resonant eigenvalues (preprint).

Hartman, 1964, Ordinary Differential Equations

10.1007/978-3-642-86458-2_37

10.1007/978-1-4612-9892-2

Bohr, 1951, Almost Periodic Functions

10.1007/BF01048789

10.1090/pspum/045.2/843604

5 Chow S. N. , Deng B. and Terman D. . The bifurcation of a homoclinic orbit from two heteroclinic orbits—a topological approach (preprint).

10.1016/S0196-8858(82)80012-2

Silnikov, 1965, A case of the existence of a countable number of periodic motions, Soviet Math. Dokl., 6, 163

6 Chow S. N. , Deng B. and Terman D. . The bifurcation of a homoclinic and a periodic orbit from two heteroclinic orbits—an analytic approach. SIAM J. App. Math. (to appear).

10.1007/BF01790539

10.1016/0022-0396(87)90034-9

10.1017/S0308210500018916

3 Chow S. N. and Deng B. . Homoclinic and heteroclinic bifurcation in Banach spaces (preprint).

10.1016/0022-0396(80)90104-7

Schwartz, 1969, Nonlinear Functional Analysis

10.1016/0022-0396(86)90032-X

Hartman, 1960, On local homeomorphisms of Euclidean spaces, Bol. Soc. Mat. Mexicana, 5, 220

10.1016/0022-0396(86)90048-3

Guckenheimer, 1983, Applied Mathematical Sciences, 42

Schecter, 1971, Principles of functional analysis

Silnikov, 1967, The existence of a denumerable set of periodic motions in four-dimensional space in an extended neighborhood of a saddle-focus, Soviet Math. Dokl., 8, 54

10.1070/SM1968v006n03ABEH001069

10.1070/SM1970v010n01ABEH001588

10.1007/BFb0103264

10.1007/BF03167912

10.1016/0022-0396(86)90043-4