Scattering solutions for planar singular Hamiltonian systems via minimization (Q5954428)

The authors consider a second order ODE of the form \({\ddot q} + \nabla V (q) = 0\), with \(q \in {\mathbb R}^2\) and \(V(q)\) a potential with two singularities located at points \(\xi_1 , \xi_2 \in {\mathbb R}^2\). NEWLINENEWLINENEWLINEThey show that in this case the system admits a large class of unbounded solutions; in particular among these is a family of solutions corresponding to each pair of entering and leaving directions and each homotopy class. This family also gives rise, via a limiting procedure, to solutions with prescribed entering angles and asymptotic to a prescribed periodic solution. NEWLINENEWLINENEWLINEThe authors also investigate chaotic solutions, in particular showing the existence of bounded ones and semibounded ones with prescribed entering angles.