## Closed orbits of fixed energy for singular Hamiltonian systems.(English)Zbl 0737.70008

The paper studies the classical $$N$$-dimensional Newtonian equations of motion in a potential field on an energy surface. The assumptions are that the potential is $$C^2$$ away from the origin where it has a singularity. If the potential behaves like $$-|x|^{-a}$$ with $$a>2$$ the existence of periodic solutions without collisions is proved. If the potential behaves like $$-|x| ^{-b}$$ with $$0<b<2$$ the existence of periodic solutions that can pass through the collision is proved.

### MSC:

 70H05 Hamilton’s equations 37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems 37G99 Local and nonlocal bifurcation theory for dynamical systems
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### References:

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