3 papers
math.DS2025
Equivalence of Rigid Motions and Relative Equilibria in the N-Body Problem on the Two-Sphere
Toshiaki Fujiwara, Ernesto Pérez-Chavela, Shuqiang Zhu
We investigate the relationship between rigid motions and relative equilibria in the N-body problem on the two-dimensional sphere, S2. We prove that any rigid motion of the N-body…
math.CA2024
Continuations and bifurcations of relative equilibria for the positive curved three body problem
Toshiaki Fujiwara, Ernesto Pérez-Chavela
The positive curved three body problem is a natural extension of the planar Newtonian three body problem to the sphere . In this paper we study the extensions of the…
math.DS2024
Periodic orbits near collision in a restricted four-body problem for the eight choreography
Abimael Bengochea, Jaime Burgos-GarcÃa, Ernesto Pérez-Chavela
We study orbits near collision in a non-autonomous restricted planar four-body problem. This restricted problem consists of a massless particle moving under the gravitational influ…