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.

中文翻译：

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矩阵序列的可约集

我们的主要目的是给还原集矩阵的序列，其变成是所述的连续1参数家庭一个完整的表征˚F _σ -Sets。我们还表明，对于任何˚F _σ 包含零-set，人们可以找到与此还原集的家庭。此外，我们获得了有关可约性-稳定性集的相应结果，并根据李雅普诺夫指数给出了对角矩阵可约性的最佳条件。