Immersion in Complex Dynamical Systems with Ergodicity
This work delves into the theory of dynamic systems, focusing on the analysis of entropy in both classical and topological contexts. Beginning with an exposition of fundamental concepts in dynamical systems theory, particular attention is given to topological dynamical systems (TDS). The discussion...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Universidade Federal de Viçosa (UFV)
2024-04-01
|
| Series: | The Journal of Engineering and Exact Sciences |
| Subjects: | |
| Online Access: | https://periodicos.ufv.br/jcec/article/view/18642 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832569830808485888 |
|---|---|
| author | Rômulo Damasclin Chaves dos Santos Jorge Henrique de Oliveira Sales |
| author_facet | Rômulo Damasclin Chaves dos Santos Jorge Henrique de Oliveira Sales |
| author_sort | Rômulo Damasclin Chaves dos Santos |
| collection | DOAJ |
| description |
This work delves into the theory of dynamic systems, focusing on the analysis of entropy in both classical and topological contexts. Beginning with an exposition of fundamental concepts in dynamical systems theory, particular attention is given to topological dynamical systems (TDS). The discussion progresses to explore discrete topological entropy and its significance within dynamical systems, culminating in the introduction of topological entropy pressure as a nuanced form of this concept. The study then investigates various applications of topological entropy within dynamic systems, emphasizing its utility in understanding chaotic systems and its role in ergodic theory. A novel theory, termed Topological Ergodic Entropy Theory (TEET), is presented, offering a fresh perspective on the analysis of ergodic dynamical systems. Furthermore, the work introduces the Ergodic Theory of Turbulent Flow (ETTF), which probes the interplay between topological entropy and the ergodic properties of dynamic systems governed by the Navier-Stokes equations. Through these explorations, the findings contribute significantly to the comprehension of the intricate nature of dynamical systems and their diverse applications across mathematics and physics. By scrutinizing topological entropy and its implications in dynamical systems, this research offers novel insights into the chaotic and stochastic behaviors exhibited by these systems. Additionally, the introduction of pioneering theories like ETTF opens up new avenues for understanding and modeling turbulent phenomena, thereby enriching our understanding of complex dynamical processes.
|
| format | Article |
| id | doaj-art-d161ae1a6e8e4217a61641af5453efca |
| institution | Kabale University |
| issn | 2527-1075 |
| language | English |
| publishDate | 2024-04-01 |
| publisher | Universidade Federal de Viçosa (UFV) |
| record_format | Article |
| series | The Journal of Engineering and Exact Sciences |
| spelling | doaj-art-d161ae1a6e8e4217a61641af5453efca2025-02-02T19:53:50ZengUniversidade Federal de Viçosa (UFV)The Journal of Engineering and Exact Sciences2527-10752024-04-0110510.18540/jcecvl10iss5pp18642Immersion in Complex Dynamical Systems with ErgodicityRômulo Damasclin Chaves dos Santos0Jorge Henrique de Oliveira Sales1Department of Physics, Technological Institute of Aeronautics, São Paulo, BrazilState University of Santa Cruz – Department of Exact Sciences, Ilhéus, Bahia, Brazil This work delves into the theory of dynamic systems, focusing on the analysis of entropy in both classical and topological contexts. Beginning with an exposition of fundamental concepts in dynamical systems theory, particular attention is given to topological dynamical systems (TDS). The discussion progresses to explore discrete topological entropy and its significance within dynamical systems, culminating in the introduction of topological entropy pressure as a nuanced form of this concept. The study then investigates various applications of topological entropy within dynamic systems, emphasizing its utility in understanding chaotic systems and its role in ergodic theory. A novel theory, termed Topological Ergodic Entropy Theory (TEET), is presented, offering a fresh perspective on the analysis of ergodic dynamical systems. Furthermore, the work introduces the Ergodic Theory of Turbulent Flow (ETTF), which probes the interplay between topological entropy and the ergodic properties of dynamic systems governed by the Navier-Stokes equations. Through these explorations, the findings contribute significantly to the comprehension of the intricate nature of dynamical systems and their diverse applications across mathematics and physics. By scrutinizing topological entropy and its implications in dynamical systems, this research offers novel insights into the chaotic and stochastic behaviors exhibited by these systems. Additionally, the introduction of pioneering theories like ETTF opens up new avenues for understanding and modeling turbulent phenomena, thereby enriching our understanding of complex dynamical processes. https://periodicos.ufv.br/jcec/article/view/18642Entropy.Topological Pressure.Ergodicity.Turbulence in Fluids.Complex Dynamic Systems. |
| spellingShingle | Rômulo Damasclin Chaves dos Santos Jorge Henrique de Oliveira Sales Immersion in Complex Dynamical Systems with Ergodicity The Journal of Engineering and Exact Sciences Entropy. Topological Pressure. Ergodicity. Turbulence in Fluids. Complex Dynamic Systems. |
| title | Immersion in Complex Dynamical Systems with Ergodicity |
| title_full | Immersion in Complex Dynamical Systems with Ergodicity |
| title_fullStr | Immersion in Complex Dynamical Systems with Ergodicity |
| title_full_unstemmed | Immersion in Complex Dynamical Systems with Ergodicity |
| title_short | Immersion in Complex Dynamical Systems with Ergodicity |
| title_sort | immersion in complex dynamical systems with ergodicity |
| topic | Entropy. Topological Pressure. Ergodicity. Turbulence in Fluids. Complex Dynamic Systems. |
| url | https://periodicos.ufv.br/jcec/article/view/18642 |
| work_keys_str_mv | AT romulodamasclinchavesdossantos immersionincomplexdynamicalsystemswithergodicity AT jorgehenriquedeoliveirasales immersionincomplexdynamicalsystemswithergodicity |