Plane rotability exponents of a linear system of differential equations

For a linear system of ordinary differential equations, we examine various exponents of Lyapunov type characterizing the rotation of solutions in some specially selected planes of solutions, namely, the planes in which this rotation is most prominent. A number of theorems are proved with regard to these new exponents being well-defined, their ordering and their relation to previously known Lyapunov characteristics of solutions, their spectra in the case of two-dimensional systems, and their relation to the eigenvalues of the operators associated with autonomous systems.