Rabinowitz, Paul H. Heteroclinics for a Hamiltonian system of double pendulum type. (English) Zbl 0898.34048 Topol. Methods Nonlinear Anal. 9, No. 1, 41-76 (1997). 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. Reviewer: Ale Jan Homburg (Berlin) Cited in 2 ReviewsCited in 4 Documents 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 Keywords:double pendulum; heteroclinic connections; periodic orbit; existence PDFBibTeX XMLCite \textit{P. H. Rabinowitz}, Topol. Methods Nonlinear Anal. 9, No. 1, 41--76 (1997; Zbl 0898.34048) Full Text: DOI