A General Framework for Splitting Concepts for Cocycles over Generalized Nonautonomous Dynamical Systems. (26th January 2017)

• Record Type: Journal Article
• Authors: Stoica, Codruţa
• Other Names: Mino Hiroyuki Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2017(2017)
• Publication Date: 2017-01-26
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2017/4790679
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : 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.