Approaching the Discrete Dynamical Systems by means of Skew-Evolution Semiflows. (12th July 2016)

• Record Type: Journal Article
• Authors: Stoica, Codruţa
• Other Names: Peterson Allan C. Academic Editor.
• Is Part Of: Discrete dynamics in nature and society. Volume 2016(2016)
• Publication Date: 2016-07-12
• Subjects: System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/2016/4375069
• Languages: English
• ISSNs: 1026-0226

Abstract

Abstract : The aim of this paper is to highlight current developments and new trends in the stability theory. Due to the outstanding role played in the study of stable, instable, and, respectively, central manifolds, the properties of exponential dichotomy and trichotomy for evolution equations represent two domains of the stability theory with an impressive development. Hence, we intend to construct a framework for an asymptotic approach of these properties for discrete dynamical systems using the associated skew-evolution semiflows. To this aim, we give definitions and characterizations for the properties of exponential stability and instability, and we extend these techniques to obtain a unified study of the properties of exponential dichotomy and trichotomy. The results are underlined by several examples.