Explorations for alternating FPU-chains with large mass

Abstract

We show interaction between high- and low-frequency modes in periodic $\alpha$-FPU chains with alternating large masses. The treatment discusses the difficult case where the number of particles $N=2p$ involves $p$ prime. A key role is played by identifying symmetric invariant manifolds, thus reducing the dimension of the problems drastically, and a Mathematica programme focused on these systems. We could show explicitly interaction for systems up to 100 particles with in addition strong arguments for interactions in arbitrary large chains.