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Statement of the main result. We study a two-center two-body problem. Consider two xed centers Q1 and Q2 of masses m1 = m2 = 1 located at distance from each other and two small particles Q3 and Q4...
The (planar) ERTBP describes the motion of a massless particle (a comet) under the gravitational field of two massive bodies (the primaries, say the Sun and Jupiter) revolving around their center of m...
The classical principle of least action says that orbits of mechanical systems extremize action; an important subclass are those orbits that minimize action. In this paper we utilize this principle al...
The purpose of this paper is twofold. First we show that the dynamics ofa Sun-Jupiter-Comet system and under some simplifying assumptions has a semi-infiniteregion of instability. This is done by redu...
A continuum of periodic solutions to the planar four-body problem with various choices of masses.
New Developments of Variational Method of N-bodym Problem in Celestial Mechanics.
Trace formula for the Sturm-Liouville eigenvalue problem with its applications to n-body problem.
Escape, collisions and regularization in the variational approach to the N-body problem.
The course is a short introduction to some aspects of the simplest non-integrable three body problem, the study of which goes back to the seminal works of Hill, Poincar′e and Birkhoff. After Goursat (...
Abstract: Donald Saari conjectured that the $N$-body motion with constant configurational measure is a motion with fixed shape. Here, the configurational measure $\mu$ is a scale invariant product of ...
We consider the planar three body problem of planetary type and we study the generation and continuation of periodic orbits and mainly of asymmetric periodic orbits.
In the 2-dimensional n-body problem in spaces of constant curvature,  6= 0, with n ≥ 3, we study polygonal homographic solutions.
The quantum $N$-body problem is studied in the context of nonrelativistic quantum mechanics with a one-dimensional deformed Heisenberg algebra of the form $[\hat x,\hat p]=i(1+\beta \hat p^2)$, leadin...
We investigate the post-Newtonian effects on Lagrange’s equilateral triangular solution for the three-body problem. It is concluded that the equilateral triangular configuration can satisfy the post-N...
Continuing work initiated in an earlier publication [Yamada, Asada, Phys. Rev. D 82, 104019 (2010)], we investigate collinear solutions to the general relativistic three-body problem. We prove the un...

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