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Non-integrability of restricted two body problems in constant curvature spaces. (English) Zbl 1048.37052
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.

37J30 Obstructions to integrability for finite-dimensional Hamiltonian and Lagrangian systems (nonintegrability criteria)
70H07 Nonintegrable systems for problems in Hamiltonian and Lagrangian mechanics
34M35 Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms
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