Indefinite Descriptive Proximities Inherent in Dynamical Systems. An Axiomatic Approach

Fuente: arXiv
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Autores principales: Peters, James Francis, Vergili, Tane, Ucan, Fatih, Vakeesan, Divagar
Formato: Preprint
Publicado: 2025
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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.
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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