Integrability of natural Hamiltonian systems with homogeneous potentials of degree zero

Details Integrability of natural Hamiltonian systems with homogeneous potentials of degree zero Integrability of natural Hamiltonian systems with homogeneous potentials of degree zero

2009-03-30

arxiv.org/abs/0903.5199v1

Phys. Lett. A., vol 374, no 3, 448--452, (2010)

Mathematics

Dynamical Systems

13 pages

Scientific paper

We derive necessary conditions for integrability in the Liouville sense of natural Hamiltonian systems with homogeneous potential of degree zero. We derive these conditions through an analysis of the differential Galois group of variational equations along a particular solution generated by a non-zero solution $\vd\in\C^n$ of nonlinear equations $\grad V(\vd)=\vd$. We proved that if the system integrable then the Hessian matrix $V''(\vd)$ has only integer eigenvalues and is semi-simple.

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