Geodesic
On the stability of the two-link trajectory of the parabolic Birkhoff billiards
Russian journal of nonlinear dynamics, Tome 12 (2016) no. 1, pp. 75-90

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We study the inertial motion of a material point in a planar domain bounded by two coaxial parabolas. Inside the domain the point moves along a straight line, the collisions with the boundary curves are assumed to be perfectly elastic. There is a two-link periodic trajectory, for which the point alternately collides with the boundary parabolas at their vertices, and in the intervals between collisions it moves along the common axis of the parabolas. We study the nonlinear problem of stability of the two-link trajectory of the point.
Keywords: map, canonical transformations, Hamilton system, stability. 
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     author = {A. P. Markeev},
     title = {On the stability of the two-link trajectory of the parabolic {Birkhoff} billiards},
     journal = {Russian journal of nonlinear dynamics},
     pages = {75--90},
     publisher = {mathdoc},
     volume = {12},
     number = {1},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ND_2016_12_1_a4/}
}
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A. P. Markeev. On the stability of the two-link trajectory of the parabolic Birkhoff billiards. Russian journal of nonlinear dynamics, Tome 12 (2016) no. 1, pp. 75-90. http://geodesic.mathdoc.fr/item/ND_2016_12_1_a4/