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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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