  We associate with each simple Lie algebra a system of second-order
differential equations invariant under a non-compact real form of the
corresponding Lie group. In the limit of a contraction to a Schr\"odinger
algebra, these equations reduce to a system of ordinary harmonic oscillators.
We provide two clarifying examples of such deformed oscillators: one system
invariant under SO(2,3) transformations, and another system featuring
$G_{2(2)}$ symmetry. The construction of invariant actions requires adding
semi-dynamical degrees of freedom; we illustrate the algorithm with the two
examples mentioned.
