Classification of fixed points of Potts–Bethe Mapping of degree four on Q5

Mohd Ali Khameini Ahmad, and Alp, Murat and Mohammad Azim Mohd Azahari, and Ahmad Fadillah Embong, (2024) Classification of fixed points of Potts–Bethe Mapping of degree four on Q5. Journal of Quality Measurement and Analysis, 20 (2). pp. 105-110. ISSN 2600-8602

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Abstract

The Potts–Bethe mapping is a rational function arises in the study of the Potts model on the Cayley tree (or Bethe lattice). In this paper, the Potts–Bethe mapping of degree four is considered over the field Q5 of 5-adic numbers. In some regimes (a condition appear in the study of p-adic Potts model), the fixed points are found and their stability are determined. It is done by solving some quartic equation over Q5 and calculating the value of derivative at each fixed points. This is the continuation of the previous work where contraction and chaos are found, but here other property is realized such as 1-Lipschitz.

Item Type:Article
Keywords:Rational function; p-adic number; Fixed point
Journal:Journal of Quality Measurement and Analysis
ID Code:24107
Deposited By: Mr. Mohd Zukhairi Abdullah
Deposited On:04 Sep 2024 08:13
Last Modified:06 Sep 2024 00:56

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