  One of the fundamental tasks in the study of dynamical systems is the
discrimination between regular and chaotic behavior. Over the years several
methods of chaos detection have been developed. Some of them, such as the
construction of the system's Poincar\'e Surface of Section, are appropriate for
low-dimensional systems. However, an enormous number of real-world problems are
described by high-dimensional systems. Thus, modern numerical methods like the
Smaller (SALI) and the Generalized (GALI) Alignment Index, which can also be
used for lower-dimensional systems, are appropriate for investigating regular
and chaotic motion in high-dimensional systems. In this work, we numerically
investigate the behavior of the GALIs in the neighborhood of simple stable
periodic orbits of the well-known Fermi-Pasta-Ulam-Tsingou lattice model. In
particular, we study how the values of the GALIs depend on the width of the
stability island and the system's energy. We find that the asymptotic GALI
values increase when the studied regular orbits move closer to the edge of the
stability island for fixed energy, while these indices decrease as the system's
energy increases. We also investigate the dependence of the GALIs on the
initial distribution of the coordinates of the deviation vectors used for their
computation and the corresponding angles between these vectors. In this case,
we show that the final constant values of the GALIs are independent of the
choice of the initial deviation vectors needed for their computation.
