Indefinite proximities inherent in dynamical systems: An axiomatic approach

Peters J. F., Vergili T., Uçan F., Vakeesan D.

Modern Mathematical Methods, sa.4, ss.134-148, 2026 (Hakemli Dergi)

Özet

  • This paper introduces indefinite proximities inherent in everThis paper introduces indefinite proximities inherent in every collection of physical objects found in adynamical system. The number of characteristics in the description of any dynamical system is unknown (Axiom 2.1and Axiom 2.2). Hence, the description of a dynamical system is indefinite. Axiomatically, these indefinite proximitieslead to a new form of Hausdorff topology, which is indefinite descriptively. The main results in this paper are1. 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 stableand that have low energy dissipation.y collection of physicalThis paper introduces indefinite proximities inherent in every collection of physical objects found in adynamical system. The number of characteristics in the description of any dynamical system is unknown (Axiom 2.1and Axiom 2.2). Hence, the description of a dynamical system is indefinite. Axiomatically, these indefinite proximitieslead to a new form of Hausdorff topology, which is indefinite descriptively. The main results in this paper are1. 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 stableand that have low energy dissipation.objects found in adynamical system. The number of characteristics in the description of any dynamical system is unknown (Axiom 2.1and Axiom 2.2). Hence, the description of a dynamical system is indefinite. Axiomatically, these indefinite proximitieslead to a new form of Hausdorff topology, which is indefinite descriptively. The main results in this paper are1. 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 stableand that have low energy dissipation.