Lyapunov functions for dichotomies in mean
Texas State University, Department of Mathematics
We consider the notion of an exponential dichotomy in mean for a cocycle, in which the exponential behavior in the classical notion of an exponential dichotomy is replaced by an average with respect to an invariant probability measure. We give a complete characterization of the exponential behavior in mean in terms of Lyapunov functions, both for cocycles over maps and flows.
Exponential dichotomies in mean, Lyapunov functions
Barreira, L., & Valls, C. (2017). Lyapunov functions for dichotomies in mean. <i>Electronic Journal of Differential Equations, 2017</i>(252), pp. 1-12.