Reducibility sets for sequences of matrices

Abstract

Our main aim is to give a complete characterization of the reducibility sets of continuous 1-parameter families of sequences of matrices, which turn out to be the F_σ -sets. We also show that for any F_σ -set containing zero, one can find a family with this reducibility set. In addition, we obtain corresponding results for the reducibility-stability set and we give an optimal condition for the reducibility to a diagonal matrix in terms of the Lyapunov exponents.