Geodesic
Discrete Lyapunov theory for evolution families
Claudia Luminita Mihit1 ; Petre Preda1 ; Claudia Luminita Mihit ; Petre Preda
1Department of Mathematics, West University of Timisoara
Acta mathematica Universitatis Comenianae, Tome 84 (2015) no. 1, pp. 149-166 
Claudia Luminita Mihit; Petre Preda; Claudia Luminita Mihit; Petre Preda. Discrete Lyapunov theory for evolution families. Acta mathematica Universitatis Comenianae, Tome 84 (2015) no. 1, pp. 149-166. http://geodesic.mathdoc.fr/item/AMUC_2015_84_1_a12/
@article{AMUC_2015_84_1_a12,
     author = {Claudia Luminita Mihit and Petre Preda and Claudia Luminita Mihit and Petre Preda},
     title = { Discrete {Lyapunov} theory for evolution families},
     journal = {Acta mathematica Universitatis Comenianae},
     pages = {149--166},
     year = {2015},
     volume = {84},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2015_84_1_a12/}
}
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Voir la notice de l'article provenant de la source Comenius University

The aim of the paper "Discrete Lyapunov theory for evolution families" is to obtain some necessary and sufficient conditions for uniform exponential dichotomy, in the discrete case for C_0-semigroups, differential systems and abstract evolution families in Hilbert spaces. We prove firstly the discrete versions of some theorems from the continuous case from P. Preda, M. Megan, Exponential dichotomy of strongly discontinuous semigroups, Bull. Austral. Math. Soc. 30(1984), 435-448, P. Preda, M. Megan, Exponential Dichotomy of Evolutionary Processes in Banach Spaces, Czechoslovak Math. J. 35(1985), 312-323 and we use them to obtain the results of Lyapunov type.