  The study of non-linear oscillator chains in classical many-body dynamics has
a storied history going back to the seminal work of Fermi, Pasta, Ulam and
Tsingou (FPUT). We introduce a new family of such systems which consist of
chains of $N$ harmonically coupled particles with the non-linearity introduced
by confining the motion of each individual particle to a box/stadium with hard
walls. The stadia are arranged on a one dimensional lattice but they
individually do not have to be one dimensional thus permitting the introduction
of chaos already at the lattice scale. For the most part we study the case
where the motion is entirely one dimensional. We find that the system exhibits
a mixed phase space for any finite value of $N$. Computations of Lyapunov
spectra at randomly picked phase space locations and a direct comparison
between Hamiltonian evolution and phase space averages indicate that the
regular regions of phase space are not significant at large system sizes. While
the continuum limit of our model is itself a singular limit of the integrable
sinh-Gordon theory, we do not see any evidence for the kind of non-ergodicity
famously seen in the FPUT work. Finally, we examine the chain with particles
confined to two dimensional stadia where the individual stadium is already
chaotic, and find a much more chaotic phase space at small system sizes.
