Indefinite proximities inherent in dynamical systems: An axiomatic approach
DOI:
https://doi.org/10.64700/mmm.87Keywords:
Characteristic, descriptive proximity space, dynamical system, Hilbert envelope, indefiniteAbstract
This paper introduces indefinite proximities inherent in every collection of physical objects found in a dynamical system. The number of characteristics in the description of any dynamical system is unknown (Axiom 2.1 and Axiom 2.2). Hence, the description of a dynamical system is indefinite. 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 3.1).
2. Every dynamical system has an indefinite descriptive Hausdorff topology (Theorem 3.3).
3. The energy of a dynamical system varies with every clock tick (Theorem 5.4).
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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Copyright (c) 2026 James Peters, Tane Vergili, Fatih Ucan, Divagar Vakeesan
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