Bohl exponents and baire classes of functions

Bohl exponents of a linear homogeneous system of differential equations are considered as functions of a parameter on its right-hand side which continuously depends on this parameter. It is shown that the Bohl exponents can be of the second or the fourth Baire class, according to the type of exponent. A similar result is established for Bohl exponents of diffeomorphisms of a Riemannian manifold.