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International Journal of Differential Equations
Volume 2013, Article ID 761680, 7 pages
http://dx.doi.org/10.1155/2013/761680
Research Article

On ( )-Dichotomies for Nonautonomous Linear Difference Equations in Banach Spaces

1Department of Mathematics, Faculty of Mathematics and Computer Science, West University of Timişoara, V. Pârvan Boulevard. no. 4, 300223 Timişoara, Romania
2Academy of Romanian Scientists, Independenţei 54, 050094 Bucharest, Romania

Received 30 April 2013; Revised 2 August 2013; Accepted 5 August 2013

Academic Editor: Timothy R. Marchant

Copyright © 2013 Mihai Gabriel Babuţia et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper considers two general concepts of dichotomy for noninvertible and nonautonomous linear discrete-time systems in Banach spaces. These concepts use two types of dichotomy projections sequences (invariant and strongly invariant) and generalize some well-known dichotomy concepts (uniform, nonuniform, exponential, and polynomial). In the particular case of strongly invariant dichotomy projections, we present characterizations of these sequences and connections with other dichotomy concepts existent in the literature. Some illustrative examples clarify the implications between these concepts.