There are many integrable ordinary differential equations that may be derived as isomonodromic deformations. Symplectic geometry gives us insight into how such system possesses a Hamiltonian description. Analogously, there are many integrable ordinary difference equations that are derived as discrete isomonodromic deformations and connection preserving deformations. By considering a geometric setting for differential and difference Lax pairs, we present some preliminary work that suggests the evolution of these systems possesses an analogous description.
