Abstract

For a non-autonomous dynamics defined by a sequence of matrices, we consider the notion of a non-uniform exponential trichotomy for an arbitrary growth rate (this means that there may exist contracting, expanding and neutral directions with an arbitrary fixed growth rate). The purpose of our work is two-fold: to use a regularity coefficient in order to show that these trichotomies occur naturally and to provide several alternative characterizations of those for which the non-uniform part is arbitrarily small. This includes characterizations in terms of the growth rate of volumes and of the Lyapunov exponents of the dynamics and its adjoint. We also obtain sharp lower and upper bounds for the regularity coefficient.

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