Geodesic
The interaction of resonances of the third and fourth orders in a Hamiltonian two-degree-of-freedom system
Russian journal of nonlinear dynamics, Tome 11 (2015) no. 4, pp. 671-683

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The motion of a time-periodic two-degree-of-freedom Hamiltonian system in the neighborhood of the equilibrium being stable in the linear approximation is considered. The weak Raman thirdorder resonance and the strong fourth-order resonance are assumed to occur simultaneously in the system. The behavior of the approximated (model) system is studied in the stability domain of the fourth-order resonance. Areas of the parameters (coefficients of the normalized Hamiltonian) are found for which all motions of the system are bounded if they begin in a sufficiently small neighborhood of the equilibrium. Boundedness domain estimate is obtained. А disturbing effect of the double resonance on the motion of the system within the boundedness domain is described.
Keywords: Hamiltonian system, canonical transformation, method of normal forms, double resonance, stability. 
@article{ND_2015_11_4_a3,
     author = {O. V. Kholostova},
     title = {The interaction of resonances of the third and fourth orders in a {Hamiltonian} two-degree-of-freedom system},
     journal = {Russian journal of nonlinear dynamics},
     pages = {671--683},
     publisher = {mathdoc},
     volume = {11},
     number = {4},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ND_2015_11_4_a3/}
}
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O. V. Kholostova. The interaction of resonances of the third and fourth orders in a Hamiltonian two-degree-of-freedom system. Russian journal of nonlinear dynamics, Tome 11 (2015) no. 4, pp. 671-683. http://geodesic.mathdoc.fr/item/ND_2015_11_4_a3/