Connecting orbits for a class of singular time-periodic second-order Hamiltonian systems

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We show the existence of connecting orbits for a class of singular second-order Hamiltonian systems where, as opposed to most of the existing literature, we assume that the potential V has not one but any finite number of maxima of equal value. We use variational methods under the assumption that V (t, u) satisfies the so-called 'strong-force' condition at the singularity. © 2016 Royal Society of Edinburgh.