16 citations · 33 across the 10 of their papers we have counts for
10 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 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…
Linear stability of periodic three-body orbits with zero angular momentum and topological dependence of Kepler's third law: a numerical test
V. Dmitrašinović, Ana Hudomal, Mitsuru Shibayama +1
We test numerically the recently proposed linear relationship between the scale-invariant period , and the topology of an orbit, on several hundred plan…
Non-integrability criterion for homogeneous Hamiltonian systems via blowing-up technique of singularities
Mitsuru Shibayama
It is a big problem to distinguish between integrable and non-integrable Hamiltonian systems. We provide a new approach to prove the non-integrability of homogeneous Hamiltonian sy…
Variational proof of the existence of the super-eight orbit in the four-body problem
Mitsuru Shibayama
Using the variational method, Chenciner and Montgomery (2000 Ann. Math. 152 881--901) proved the existence of an eight-shaped periodic solution of the planar three-body problem wit…