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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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2016/4375069 |
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| _version_ | 1832558347537088512 |
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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. |
| format | Article |
| id | doaj-art-d582e35d49334a21b7f4a7c76e3bfb75 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| 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 |