Naslov
On the Asymptotic Behavior of Discrete Dynamical Systems - An Ergodic Theory Approach

Autori
Dragičević, Davor ; Sasu, Adina Luminita ; Sasu, Bogdan

Izvornik
Journal of differential equations (0022-0396) 268 (2020), 5; 4786-4829

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Uniform exponential stability ; Uniform exponential expansiveness ; Uniform exponential dichotomy ; Input-output system ; Admissibility

Sažetak
The aim of this paper is to present a new and general method for the study of stability, expansiveness and dichotomy of dynamical systems, based on arguments proceeding from ergodic theory and on admissibility properties. We consider a discrete variational system and we associate to it three different families of input-output systems corresponding to the investigations for stability, expansiveness and dichotomy, respectively. We introduce some input-output conditions relative to ergodic measures and we show that certain nonuniform admissibility properties imply the existence of the uniform asymptotic behaviors. First, we obtain characterizations for uniform exponential stability. As an application, we prove that in order to preserve the uniform exponential stability subject to perturbations it is sufficient for the perturbed system to be close enough to the initial system on a measurable set. Next, we deduce criteria for uniform exponential expansiveness based on some exact admissibilities relative to ergodic measures. Finally, we present an interesting application to the study of the uniform exponential dichotomy, starting from a nonuniform admissibility property and using stability criteria.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA