Explorations for alternating FPU-chains with large mass

Abstract

We show interaction between high- and low-frequency modes in periodic α-FPU chains with alternating large masses. This high-low frequency interaction is known if the number of particles N is a 4-fold, our 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 show explicitly high-low frequency interaction for systems with 2pn particles where 2≤p≤47 is prime and n is an arbitrary natural number. In addition we have strong arguments for interactions in arbitrary large chains.