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arXiv · 2501.02585

Indefinite Descriptive Proximities Inherent in Dynamical Systems. An Axiomatic Approach

James Francis Peters·Tane Vergili·Fatih Ucan·Divagar Vakeesan
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Abstract

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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James Francis Peters, Tane Vergili, Fatih Ucan, Divagar Vakeesan. 2025-01-05. Indefinite Descriptive Proximities Inherent in Dynamical Systems. An Axiomatic Approach. https://arxiv.org/abs/2501.02585

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