Non-integrability of restricted two body problems in constant curvature spaces
The authors consider a restricted problem of two bodies in constant curvature spaces. The Newton and Hooke interactions between bodies are considered. For both types of interactions, the authors prove the nonintegrability of this problem in spaces with constant nonzero curvature. Their proof is based on the Morales-Ramis theory.
scientific article; zbMATH DE number 2097050