Geodesic
Basic bifurcation scenarios in neighborhoods of boundaries of stability regions of libration points in the three-body problem
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential equations. Mathematical physics, Tome 139 (2017), pp. 114-127 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper, we construct stability regions (in the linear approximation) of triangular libration points for the planar, bounded, elliptical three-body problem and examine bifurcations that occur when parameters of the system pass through the boundaries of these regions. A new scheme for the construction of stability regions is presented, which leads to approximation formulas describing these boundaries. We prove that on one part of the boundary, the main scenario of bifurcation is the appearance of nonstationary $4\pi$-periodic solutions that are close to a triangular libration point, whereas on the other part, the main scenario is the appearance of quasiperiodic solutions.
Keywords: three-body problem, libration point, stability, stability region, periodic solutions, parameter.
Mots-clés : bifurcation 
@article{INTO_2017_139_a10,
     author = {M. G. Yumagulov},
     title = {Basic bifurcation scenarios in neighborhoods of boundaries of stability regions of libration points in the three-body problem},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {114--127},
     year = {2017},
     volume = {139},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2017_139_a10/}
}
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M. G. Yumagulov. Basic bifurcation scenarios in neighborhoods of boundaries of stability regions of libration points in the three-body problem. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential equations. Mathematical physics, Tome 139 (2017), pp. 114-127. http://geodesic.mathdoc.fr/item/INTO_2017_139_a10/