[1]
|
S. Wiggins, “Golbal Bifurcations and Chaos,” Springer-Verlag, New York, 1988.
|
[2]
|
K. J. Palmer, “Transversal Heteroclinic Orbits and Cherry’s Example of a Nonintegrable Hamiltonian System,” Journal of Differential Equations, Vol. 65, No. 3, 1986, pp. 321-360. doi:10.1016/0022-0396(86)90023-9
|
[3]
|
K. J. Palmer, “Exponential Dichotomies and Transversal Homoclinic Points,” Journal of Differential Equations, Vol. 55, No. 2, 1984, pp. 225-256.
doi:10.1016/0022-0396(84)90082-2
|
[4]
|
S. Campbell and P. Holmes, “Bifurcation from O(2)sy Mmetric Heterclinic Cycles with Three Interacing Mofes,” Nonlinearity, Vol. 4, 1991, pp. 697-726.
|
[5]
|
K. R. Meyer and G. R. Sell, “Melnikov Transforms, Bernoulli Bundle and Almost Periodic Perturbations,” Transactions of the American Mathematical Society, Vol. 314, No. 1, 1989, pp. 63-105.
|
[6]
|
H. Kokubu, “Homoclinic and Heteroclinic Bifurcations of Vector Fields,” Japan Journal of Industrial and Applied Mathematics, Vol. 5, No. 3, 1988, pp. 455-501.
doi:10.1007/BF03167912
|
[7]
|
S. N. Chow, B. Deng and D. Terman, “The Bifurcations of a Homoclinic and a Periodic Orbit from Two Hetero- clinic Orbits,” SIAM Journal on Mathematical Analysis, Vol. 21, No. 1, 2000, pp. 179-204. doi:10.1137/0521010
|
[8]
|
J. M. Gambaudo, P. Glendinning and C. Tresser, “Collages de Cycles et Suites de Farey,” Comptes Rendus de l'Académie des Sciences, Vol. 299, 1984, pp. 711-714.
|
[9]
|
S. N. Chow, B. Deng and D. Terman, “The Bifurcation of a Homoclinic Orbit from Two Heteroclinic Orbits—A Topological Approach,” Applicable Analysis: An International Journal, Vol. 42, No. 1-4, 1991, pp. 1057-1080.
doi:10.1080/00036819108840047
|
[10]
|
X. B. Lin, “Using Melnikov’s Method to Solve Silnikov Problems,” Proceedings of the Royal Society of Edin- burgh: Section A Mathematics, Vol. 116, No. 3-4, 1990, pp. 295-325. doi:10.1017/S0308210500031528
|
[11]
|
B. Sandstede and A. Scheel, “Forced Symmetry Breaking of Homoclinic Cycles,” Nonlinearity, Vol. 8, No. 3, 2009, pp. 333-365. doi:10.1088/0951-7715/8/3/003
|
[12]
|
J. Guckenheimer and P. Holmes, “Strucarrlly Stable Pulse Heteroclinic Cycles,” Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 103, No. 1, 2008, pp. 189-192. doi:10.1017/S0305004100064732
|
[13]
|
M. Krupa and I. Melbourne, “Asymptotic Stability of Heteroclinic Cycles in Systems with Symmetry,” Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Vol. 134, No. 6, 2004, pp. 1177-1197.
doi:10.1017/S0308210500003693
|
[14]
|
M. Krupa, “Robust Heteroclinic Cycles,” Journal of Non- linear Science, Vol. 7, No. 2, 2011.
doi:10.1007/BF02677976
|
[15]
|
W. A. Coppel, “Dichotomies in Stability Theory, Lecture Notes in Mathematics,” Springer-Verlag, New York, 1978.
|
[16]
|
R. J. Sacker and G. R. Sell, “A Spectral Theory for Linear Differential Systems,” Journal of Differential Equations, Vol. 27, No. 3, 1978, pp. 320-385.
doi:10.1016/0022-0396(78)90057-8
|
[17]
|
P. Chossat, M. Krupa, I. Melbourne and A. Scheel, “Trans- verse Bifurcations of Homkoclinic Cycles,” Physica D: Nonlinear Phenomena, Vol. 100, No. 1-2, 2011, pp. 85-100. doi:10.1016/S0167-2789(96)00186-8
|
[18]
|
V. Naudot, “Hyperbolic Dynamice in the Unfolding of a Degenerate Homoclinic Orbit,” Preprint.
|
[19]
|
W. Y. Zeng, “Exponential Dichotomies and Transversal Homoclinic Orbits in Degenerate Cases,” Journal of Dynamics and Differential Equations, Vol. 7, No. 4, 1995, pp. 521-548. doi:10.1007/BF02218723
|
[20]
|
G. R. Sell, “Bifurcation of Higher Dimensional Tori,” Archive for Rational Mechanics and Analysi, Vol. 69, No. 3, 1979, pp. 199-230. doi:10.1007/BF00248134
|