Chaotic behavior of rapidly oscillating Lagrangian systems (Q1433447)

There are described some examples of functions \(\alpha\) such that the Lagrangian system \(\ddot q=\alpha (\omega t)V'(q)\), with \(t\in \mathbb R\) and \(q\in \mathbb R^N\), has a multibump solution for all \(\omega >0\) large. Here, \(V\in C^2(\mathbb R^N,\mathbb R)\) is periodic in \(q\) satisfying additional conditions. Three examples are presented when \(\alpha\) is: quasiperiodic, almost-periodic and limit periodic. Global variational methods are used.