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On dynamical behavior of the $p$-adic $\lambda$-Ising model on Cayley tree
Mutlay Dogan University of Bahamas, Faculty of Pure and Applied Sciences, Oakes Field Campus, N 4912, Nassau, Bahamas
Аннотация:
In the present paper, we continue to study some features of the mixed type $p$-adic $\lambda$-Ising model which was studied in [MD17-1]. In that study, the existence of the $p$-adic Gibbs measures and phase transitions were investigated for the model on the Cayley tree of order two. In the current paper, we study the dynamical behavior of the fixed points which have been found in [MD17-1]. As the main result, we proved that the fixed point $u_0$ is an attractor and the other fixed points $u_{1,2}$ are repellent fixed points for the mixed type $p$-adic $\lambda$-Ising model. In addition, the size of basin of attractor for the fixed point $u_0$ is described.
Ключевые слова и фразы:
$p$-adic numbers, $p$-adic quasi Gibbs measure, dynamical systems, Cayley tree.
Поступила в редакцию: 04.04.2018 Исправленный вариант: 11.06.2018
Образец цитирования:
Mutlay Dogan, “On dynamical behavior of the $p$-adic $\lambda$-Ising model on Cayley tree”, Журн. матем. физ., анал., геом., 15:3 (2019), 321–335
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/jmag730 https://www.mathnet.ru/rus/jmag/v15/i3/p321
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