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 Nelin. Dinam., 2016, Volume 12, Number 1, Pages 75–90 (Mi nd513)

Original papers

On the stability of the two-link trajectory of the parabolic Birkhoff billiards

A. P. Markeev

A.Ishlinsky Institite for Problems in Mechanics, Russian Academy of Sciences, pr. Vernadskogo 101-1, Moscow, 119526, Russia

Abstract: 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

 Funding Agency Grant Number Russian Foundation for Basic Research 14-01-00380_à

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UDC: 531.01, 531.36
MSC: 70H05, 70H15, 70E50
Revised: 22.02.2016

Citation: A. P. Markeev, “On the stability of the two-link trajectory of the parabolic Birkhoff billiards”, Nelin. Dinam., 12:1 (2016), 75–90

Citation in format AMSBIB
\Bibitem{Mar16} \by A.~P.~Markeev \paper On the stability of the two-link trajectory of the parabolic Birkhoff billiards \jour Nelin. Dinam. \yr 2016 \vol 12 \issue 1 \pages 75--90 \mathnet{http://mi.mathnet.ru/nd513} 

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This publication is cited in the following articles:
1. A. P. Markeev, “On the stability of periodic trajectories of a planar Birkhoff billiard”, Proc. Steklov Inst. Math., 295 (2016), 190–201
2. Anatoly P. Markeev, “On the Stability of Periodic Motions of an Autonomous Hamiltonian System in a Critical Case of the Fourth-order Resonance”, Regul. Chaotic Dyn., 22:7 (2017), 773–781
3. A. N. Kirillov, R. V. Alkin, “Ustoichivost periodicheskikh bilyardnykh traektorii v treugolnike”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 18:1 (2018), 25–39
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