Indefinite Descriptive Proximities Inherent in Dynamical Systems. An Axiomatic Approach
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909448576958464 |
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| author | Peters, James Francis Vergili, Tane Ucan, Fatih Vakeesan, Divagar |
| author_facet | Peters, James Francis Vergili, Tane Ucan, Fatih Vakeesan, Divagar |
| contents | This paper introduces indefinite proximities inherent in the collection of physical objects found in a dynamical system. Axiomatically, these indefinite proximities lead to a new form of Hausdorff topology, which is indefinite descriptively. The main results in this paper are (1) Every descriptive proximity space on a dynamical system is indefinite (Theorem 1), (2) Every dynamical system has an indefinite descriptive Hausdorff topology (Theorem 3), and (3) The energy of a dynamical system varies with every clock tick (Theorem 4). An application of these results is given in terms of the detection of those portions of a dynamical system that are stable and that have low energy dissipation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_02585 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Indefinite Descriptive Proximities Inherent in Dynamical Systems. An Axiomatic Approach Peters, James Francis Vergili, Tane Ucan, Fatih Vakeesan, Divagar Dynamical Systems General Topology 054E05, 54C50, 37B02 This paper introduces indefinite proximities inherent in the collection of physical objects found in a dynamical system. Axiomatically, these indefinite proximities lead to a new form of Hausdorff topology, which is indefinite descriptively. The main results in this paper are (1) Every descriptive proximity space on a dynamical system is indefinite (Theorem 1), (2) Every dynamical system has an indefinite descriptive Hausdorff topology (Theorem 3), and (3) The energy of a dynamical system varies with every clock tick (Theorem 4). An application of these results is given in terms of the detection of those portions of a dynamical system that are stable and that have low energy dissipation. |
| title | Indefinite Descriptive Proximities Inherent in Dynamical Systems. An Axiomatic Approach |
| topic | Dynamical Systems General Topology 054E05, 54C50, 37B02 |
| url | https://arxiv.org/abs/2501.02585 |