16 citations · 33 across the 10 of their papers we have counts for
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math.DS2013★ 1 cited
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…
math.DS2013★ 16 cited
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…