Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6419176 | Journal of Mathematical Analysis and Applications | 2013 | 17 Pages |
Abstract
We give a complete characterization of a general type of exponential dichotomies in terms of Lyapunov functions, both for discrete and continuous time. This includes constructing explicitly quadratic Lyapunov functions for each exponential dichotomy. We consider the general cases of nonautonomous dynamics, nonuniform exponential dichotomies and, motivated by ergodic theory, strong exponential dichotomies, in the sense that there exist simultaneously lower and upper contraction and expansion bounds. As a nontrivial application, we establish the persistence of the asymptotic stability of a strong nonuniform exponential dichotomy under sufficiently small linear perturbations.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Luis Barreira, Davor DragiÄeviÄ, Claudia Valls,