Regular and chaotic recurrence in FPU cell-chains

Abstract

In contrast to the classical Fermi-Pasta-Ulam (FPU) chain, the inhomogeneous FPU chain shows nearly all the principal resonances. Using this fact, we can construct a periodic FPU chain of low dimension, for instance a FPU cell of four degrees-of-freedom, that can be used as a building block for a FPU cell-chain. This is a new type of chain. Differences between chains in nearest-neighbor interaction and those in overall interaction are caused by symmetry. We will show some striking results on the dynamics of FPU cell-chains where near-integrable behavior or chaos plays a part near stable equilibrium.