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Heteroclinics for a Hamiltonian system of double pendulum type. (English) Zbl 0898.34048

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.

MSC:

34C37 Homoclinic and heteroclinic solutions to ordinary differential equations
37D40 Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
53D25 Geodesic flows in symplectic geometry and contact geometry
58E30 Variational principles in infinite-dimensional spaces
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
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