Geodesic
Oscillations near a separatrix in the Duffing equation
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 18 (2012) no. 2, pp. 141-153 Cet article a éte moissonné depuis la source Math-Net.Ru

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A small periodic perturbation results in a complicated dynamics near separatrices and saddle points. A two-parameter family of asymptotic solutions staying near separatrices for a long time is constructed. Solutions from this family depend nonsmoothly on the disturbance parameter. An example is given in which the values of the disturbance parameter for this family of solutions are determined by a set with structure of the type of the Cantor set.
Mots-clés : perturbation, oscillations.
Keywords: separatrix 
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O. M. Kiselev. Oscillations near a separatrix in the Duffing equation. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 18 (2012) no. 2, pp. 141-153. http://geodesic.mathdoc.fr/item/TIMM_2012_18_2_a12/

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