We study a certain type of the celebrated Fermi-Pasta-Ulam particle
chain, namely the inverted FPU model, where the inter-particle
potential has a form of a quartic double well. Numerical evidence is
given in support of a simple symbolic description of dynamics (in the
regime of sufficiently high potential barrier between the wells) in
terms of an (approximate) Markov process. The corresponding transition
matrix is formally identical to a ferromagnetic Heisenberg quantum
spin-
chain with long range coupling, whose diagonalization
yields accurate estimates for a class of time correlation functions of
the model.