Heteroclinics for a Hamiltonian system of double pendulum type (Q1380895)

The author considers a differential equation \(\ddot q=V'(q)\), where \(V\) is a \(C^2\) function on \(\mathbb{R}^2\) which is \(T_i\)-periodic in \(x_i\), \(i=1,2\). Such a system arises as a simpler model of the double pendulum. Under the assumption that a unique maximum occurs on a lattice \(\mathbb{Z}_2\), the author studies the existence of heteroclinic connections between the lattice points and from a lattice point to a periodic orbit. Conditions are given for the existence of such heteroclinic connections.