8 papers
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…
Explicit formulae and topological descriptions of action-minimizing sets of a full shift with an uncountable alphabet
Yuika Kajihara, Shoya Motonaga, Mao Shinoda
We completely solve ergodic optimization of a full shift with an uncountable alphabet , which is one of the most well-known examples of infinite dimensional dynamical system…
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…
The Aubry set for the XY model and typicality of periodic optimization for 2-locally constant potentials
Yuika Kajihara, Shoya Motonaga, Mao Shinoda
We consider the Aubry set for the XY model, symbolic dynamics with the uncountable symbol , and study its action-optimizing properties. Moreover,…
Variational Structures for Infinite Transition Orbits of Monotone Twist Maps
Yuika Kajihara
In this paper, we consider chaotic dynamics and variational structures of area-preserving maps. There is a lot of study on the dynamics of their maps and the works of Poincare and…
Variational structures for infinite transition orbits of monotone twist maps
Yuika Kajihara
In this paper, we consider chaotic dynamics and variational structures of area-preserving maps. There is a lot of study on dynamics of their maps and the works of Poincare and Birk…
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…