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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Existence of hyperbolic motions for Newtonian and generalized N-body problem（II）
牛顿 广义N体问题 双曲运动 存在性
2023/11/7
For the classical N-body problem, Maderna-Venturelli [Ann. Math. 2020] proved the existence of hyperbolic motions with any positive energy constant, starting from any configuration and along any nonco...
NON-COLLISION SINGULARITIES IN THE PLANAR TWO-CENTER-TWO-BODY PROBLEM
PLANAR TWO-CENTER-TWO-BODY PROBLEM NON-COLLISION SINGULARITIES
2015/9/29
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...
Global instability in the elliptic restricted three body problem
Elliptic Restricted Three Body problem Arnold diffusion splitting of separatrices Melnikov integral
2015/9/25
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...
DESTRUCTION OF INVARIANT CURVES IN THE RESTRICTED CIRCULAR PLANAR THREE-BODY PROBLEM BY USING COMPARISON OF ACTION
INVARIANT CURVES RESTRICTED CIRCULAR PLANAR THREE-BODY PROBLEM
2015/9/25
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 METHOD OF SPREADING CUMULATIVE TWIST AND ITS APPLICATION TO THE RESTRICTED CIRCULAR PLANAR THREE BODY PROBLEM
SPREADING CUMULATIVE TWIST RESTRICTED CIRCULAR PLANAR THREE BODY PROBLEM
2015/9/25
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
periodic solutions planar four-body problem various choices of masses
2015/3/18
A continuum of periodic solutions to the planar four-body problem with various choices of masses.
New Developments of Variational Method of N-body Problem in Celestial Mechanics
Variational Method N-body Problem Celestial Mechanics
2015/3/18
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
Sturm-Liouville eigenvalue applications n-body problem
2015/3/18
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
Escape collisions regularization variational approach N-body problem
2015/3/18
Escape, collisions and regularization in the variational approach to the N-body problem.
The planar circular restricted three body problem in the lunar case
The planar circular restricted three body problem lunar case
2015/3/18
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 (...
Saari's homographic conjecture for planar equal-mass three-body problem under a strong force potential
Saari's homographic conjecture planar equal-mass three-body problem Mathematical Physics
2011/9/1
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 ...
On the bifurcation and continuation of periodic orbits in the three-body problem
three body problem (TBP) periodic orbits bifurcations
2010/12/28
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.
Polygonal Homographic Orbits of the Curved n-Body Problem
Polygonal Homographic Orbits Curved n-Body Problem
2011/1/20
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 with a minimal length
The quantum N-body problem minimal length
2010/12/23
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...
Post-Newtonian effects on Lagrange's equilateral triangular solution for the three-body problem
Post-Newtonian effects Lagrange's equilateral triangular solution three-body problem
2010/12/20
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...