Reducibility and Generalized Reducibility of Linear Differential Systems with a Real Multiplier Parameter

Abstract We construct a pair of mutually reducible linear differential systems with bounded continuous coefficients on the time half-line with the following property: there exists a countable set of real numbers such that, for each number in this set, the systems obtained by multiplying the coefficient matrices of the original systems by that number cannot be reduced to each other but are reducible to each other in the generalized sense.