Abstract
We give two new characterizations of the notion of Lyapunov regularity in terms of the lower and upper exponential growth rates of the singular values. These characterizations motivate the introduction of new regularity coefficients. In particular, we establish relations between these regularity coefficients and the Lyapunov regularity coefficient. Moreover, we construct explicitly bounded sequences of matrices attaining specific values of the new regularity coefficients.
Highlights
The purpose of this work is twofold: to introduce new regularity coefficients and to give new characterizations of Lyapunov regularity
The notion of regularity was introduced by Lyapunov and plays an important role in the stability theory of differential equations and dynamical systems
The new characterizations of Lyapunov regularity are expressed in terms of the lower and upper exponential growth rates of the singular values
Summary
The purpose of this work is twofold: to introduce new regularity coefficients and to give new characterizations of Lyapunov regularity. The notion of regularity was introduced by Lyapunov and plays an important role in the stability theory of differential equations and dynamical systems. It is ubiquitous in the context of ergodic theory. The new characterizations of Lyapunov regularity are expressed in terms of the lower and upper exponential growth rates of the singular values
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