Geometric affine symplectic curve flows in R4R4

The method of equivariant moving frames is used to obtain the equations governing the evolution of the differential invariants of an invariant affine symplectic curve flow in R4R4 preserving arc length. Conditions guaranteeing that a geometric curve flow produces Hamiltonian evolution equations are obtained. Finally, we show that a constant tangential curve flow produces bi-Hamiltonian evolution equations.