Representations of symmetric linear dynamical systems

The symmetries of dynamical systems in a special class of dynamical systems referred to as L^q are studied. A symmetry is induced by a transformation group, the basic idea being that there is a group of transformations mapping one dynamical system Σ in L^q into another. If this transformation leaves the behavior invariant, then Σ is called symmetric. A necessary and sufficient condition for Σ to exhibit a type of symmetry called v-symmetry is obtained, and an example showing a canonical form for symmetric systems is given