From homoclinics to quasi-periodic solutions for ordinary differential equations
2015 ◽
Vol 145
(5)
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pp. 1091-1114
Keyword(s):
We consider the quasi-periodic solutions bifurcated from a degenerate homoclinic solution. Assume that the unperturbed system has a homoclinic solution and a hyperbolic fixed point. The bifurcation function for the existence of a quasi-periodic solution of the perturbed system is obtained by functional analysis methods. The zeros of the bifurcation function correspond to the existence of the quasi-periodic solution at the non-zero parameter values. Some solvable conditions of the bifurcation equations are investigated. Two examples are given to illustrate the results.
2006 ◽
Vol 73
(2)
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pp. 175-182
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1978 ◽
Vol 81
(1-2)
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pp. 131-151
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2010 ◽
Vol 82
(3)
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pp. 437-445
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1986 ◽
Vol 102
(3-4)
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pp. 259-262
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