| Abstract: |
| We discuss nonintegrability of Hamiltonian systems with homogeneous potentials of degree $-2$. Morales-Ramis theory provides sufficiently conditions for nonintegrability of homogeneous potential systems, but it can not be apply to the case that degree of potential is -2. By focusing on remarkable properties of systems, we obtain sufficiently conditions for the nonintegrability of these systems. As an application, we prove the nonintegrability of the planer three-body problem with inverse-square potential. |
|