On the Topological Dynamics of Dynamical Manifolds and Their Fundamental Group
The paper aims to deduce the relation between the category of topology and algebra from viewpoint of geometry and dynamical system. We introduce and define a dynamical manifold as a manifold associated with a time parameter. We obtain the induced chain of topological dynamics on the fundamental grou...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/5697831 |
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| _version_ | 1849691102502715392 |
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| author | M. Abu-Saleem Omar Almallah |
| author_facet | M. Abu-Saleem Omar Almallah |
| author_sort | M. Abu-Saleem |
| collection | DOAJ |
| description | The paper aims to deduce the relation between the category of topology and algebra from viewpoint of geometry and dynamical system. We introduce and define a dynamical manifold as a manifold associated with a time parameter. We obtain the induced chain of topological dynamics on the fundamental group from the chain of dynamical maps on a dynamical manifold. For many adjunctions in this context, we deduce the limit topological dynamics and conditional topological dynamics on the fundamental group. We use the category of commutative diagrams as chains of dynamical manifolds to deduce the chains on fundamental groups. Also, we describe how the manifold changes in a dynamical system from the view of the fundamental group. |
| format | Article |
| id | doaj-art-e2609a2f600842e89ae188ceac462250 |
| institution | DOAJ |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-e2609a2f600842e89ae188ceac4622502025-08-20T03:21:08ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/56978315697831On the Topological Dynamics of Dynamical Manifolds and Their Fundamental GroupM. Abu-Saleem0Omar Almallah1Department of Mathematics, Al-Balqa Applied University, Salt, JordanDepartment of Mathematics, Al-Balqa Applied University, Salt, JordanThe paper aims to deduce the relation between the category of topology and algebra from viewpoint of geometry and dynamical system. We introduce and define a dynamical manifold as a manifold associated with a time parameter. We obtain the induced chain of topological dynamics on the fundamental group from the chain of dynamical maps on a dynamical manifold. For many adjunctions in this context, we deduce the limit topological dynamics and conditional topological dynamics on the fundamental group. We use the category of commutative diagrams as chains of dynamical manifolds to deduce the chains on fundamental groups. Also, we describe how the manifold changes in a dynamical system from the view of the fundamental group.http://dx.doi.org/10.1155/2021/5697831 |
| spellingShingle | M. Abu-Saleem Omar Almallah On the Topological Dynamics of Dynamical Manifolds and Their Fundamental Group Journal of Mathematics |
| title | On the Topological Dynamics of Dynamical Manifolds and Their Fundamental Group |
| title_full | On the Topological Dynamics of Dynamical Manifolds and Their Fundamental Group |
| title_fullStr | On the Topological Dynamics of Dynamical Manifolds and Their Fundamental Group |
| title_full_unstemmed | On the Topological Dynamics of Dynamical Manifolds and Their Fundamental Group |
| title_short | On the Topological Dynamics of Dynamical Manifolds and Their Fundamental Group |
| title_sort | on the topological dynamics of dynamical manifolds and their fundamental group |
| url | http://dx.doi.org/10.1155/2021/5697831 |
| work_keys_str_mv | AT mabusaleem onthetopologicaldynamicsofdynamicalmanifoldsandtheirfundamentalgroup AT omaralmallah onthetopologicaldynamicsofdynamicalmanifoldsandtheirfundamentalgroup |