Approaching the Discrete Dynamical Systems by means of Skew-Evolution Semiflows

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 d...

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Main Author: Codruţa Stoica
Format: Article
Language:English
Published: Wiley 2016-01-01
Series:Discrete Dynamics in Nature and Society
Online Access:http://dx.doi.org/10.1155/2016/4375069
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author Codruţa Stoica
author_facet Codruţa Stoica
author_sort Codruţa Stoica
collection DOAJ
description 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.
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institution Kabale University
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publishDate 2016-01-01
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series Discrete Dynamics in Nature and Society
spelling doaj-art-d582e35d49334a21b7f4a7c76e3bfb752025-02-03T01:32:41ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2016-01-01201610.1155/2016/43750694375069Approaching the Discrete Dynamical Systems by means of Skew-Evolution SemiflowsCodruţa Stoica0Department of Mathematics and Computer Science, Aurel Vlaicu University of Arad, 2 Elena Drăgoi Street, 310330 Arad, RomaniaThe 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.http://dx.doi.org/10.1155/2016/4375069
spellingShingle Codruţa Stoica
Approaching the Discrete Dynamical Systems by means of Skew-Evolution Semiflows
Discrete Dynamics in Nature and Society
title Approaching the Discrete Dynamical Systems by means of Skew-Evolution Semiflows
title_full Approaching the Discrete Dynamical Systems by means of Skew-Evolution Semiflows
title_fullStr Approaching the Discrete Dynamical Systems by means of Skew-Evolution Semiflows
title_full_unstemmed Approaching the Discrete Dynamical Systems by means of Skew-Evolution Semiflows
title_short Approaching the Discrete Dynamical Systems by means of Skew-Evolution Semiflows
title_sort approaching the discrete dynamical systems by means of skew evolution semiflows
url http://dx.doi.org/10.1155/2016/4375069
work_keys_str_mv AT codrutastoica approachingthediscretedynamicalsystemsbymeansofskewevolutionsemiflows