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Mathematical Problems in Engineering
Volume 2017 (2017), Article ID 4790679, 8 pages
Research Article

A General Framework for Splitting Concepts for Cocycles over Generalized Nonautonomous Dynamical Systems

Department of Mathematics and Computer Science, Aurel Vlaicu University of Arad, Arad, Romania

Correspondence should be addressed to CodruĊ£a Stoica

Received 15 October 2016; Accepted 4 January 2017; Published 26 January 2017

Academic Editor: Hiroyuki Mino

Copyright © 2017 Codruţa Stoica. 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.


While the classic theory of exponential dichotomy deals with differential and difference equations with uniquely determined forward and backward solutions, nowadays, applications in engineering require having corresponding theory for equations whose backward solutions are not guaranteed to exist or to be unique. To this goal, we will consider general dichotomic behaviors that consist in assuming the existence of splitting into invariant subspaces, where the norms of the evolution trajectories are bounded by some functions that depend on the initial and final times.