5 papers
Existence of Really Perverse Central Configurations in the Spatial -Body Problem
Mitsuru Shibayama
We construct explicit examples of really perverse central configurations in the spatial Newtonian -body problem. A central configuration is called really perverse if it satisfie…
Hamiltonian systems and monotone twist mappings for braids
Yuika Kajihara, Mitsuru Shibayama
In 1986, Moser showed that for a given area-preserving map, there exists a Hamiltonian system that realizes it on the Poincaré section. Using his technique, we show that for any br…
Variational Construction of Homoclinic and Heteroclinic Orbits in the Planar Sitnikov Problem
Yuika Kajihara, Mitsuru Shibayama, Guowei Yu
The Sitnikov problem is a special case of the three-body problem. The system is known to be chaotic and has been studied by symbolic dynamics (J. Moser, Stable and random motions i…
A study of braids arising from simple choreographies of the planar Newtonian N-body problem
Yuika Kajihara, Eiko Kin, Mitsuru Shibayama
We study periodic solutions of the planar Newtonian -body problem with equal masses. Each periodic solution traces out a braid with strands in 3-dimensional space. When the…
Braids, metallic ratios and periodic solutions of the -body problem
Yuika Kajihara, Eiko Kin, Mitsuru Shibayama
Periodic solutions of the planar -body problem determine braids through the trajectory of bodies. Braid types can be used to classify periodic solutions. According to the Ni…