Abstract
As an application of the results in Chap. 6, here we give several additional characterizations of regularity, in particular in terms of the exponential growth rates of the singular values and in terms of a certain symmetrized version of the dynamics. We consider both discrete and continuous time. Moreover, for a sequence of matrices, we introduce a third regularity coefficient—the Lyapunov coefficient—and we relate it to the Grobman and Perron coefficients. Finally, we determine all pairs of nonnegative numbers that can be the Lyapunov coefficients, respectively, of a bounded sequence of matrices and its adjoint sequence. We note that an adjoint sequence has the same Grobman and Perron coefficients as the original sequence, although in general this is not the case for the Lyapunov coefficient.
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