  A Lie system is a non-autonomous system of first-order ordinary differential
equations describing the integral curves of a non-autonomous vector field
taking values in a finite-dimensional real Lie algebra of vector fields, a
so-called Vessiot--Guldberg Lie algebra. In this work, multisymplectic
structures are applied to the study of the reduction of Lie systems through
their Lie symmetries. By using a momentum map, we perform a reduction and
reconstruction procedure of multisymplectic Lie systems, which allows us to
solve the original problem by analysing several simpler multisymplectic Lie
systems. Conversely, we study how reduced multisymplectic Lie systems allow us
to retrieve the form of the multisymplectic Lie system that gave rise to them.
Our results are illustrated with examples occurring in physics, mathematics,
and control theory.
