6 papers
A Minimax Approach to Relative Periodic Orbits in Symmetric Three-Degree-of-Freedom Hamiltonian Systems
Shu Sakaguchi, Mitsuru Shibayama
We study three-degree-of-freedom Hamiltonian systems that are invariant under rotations about the -axis and under reflection across the -plane. Fixing the angular momentum,…
Invariant Curves and the Variational Structure in Tubular Origami Dynamical Systems
Ryutaro Ichikawa, Mitsuru Shibayama
We present a theoretical and numerical dynamical-systems analysis of tubular origami tessellations by identifying the inverse module number, , as a perturbation parameter w…
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 b…
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…