On Dynamical Behavior of the p-adic λ-Ising Model on Cayley Tree
DOI:
https://doi.org/10.15407/mag15.03.321Анотація
У даній статті ми продовжуємо вивчення деяких властивостей $p$-aдичної $\lambda$-ізінгової моделі змішаного типу, що вивчалася в [3]. У тій роботі існування $p$-адичних мір Гібса і фазових переходів досліджувалося в моделі на дереві Кейлі другого порядка. У даній статті ми вивчаємо динамічну поведінку нерухомих точок, які було знайдено в [3]. Основним результатом є те, що ми довели, що нерухома точка $u_0$ є атрактором, а інші нерухомі точки $u_{1,2}$ репелентними нерухомими точками для $p$-aдичної $\lambda$-ізінгової моделі змішаного типу. На додаток описано розмір басейну атрактора для нерухомої точки $u_0$.Mathematics Subject Classification: 58F12, 46S10, 12J12, 11S99, 54H20, 30D05.
Ключові слова:
p-адичнi числа, p-адична квазiмiра Гiббса, динамiчнi системи, дерево КейлiПосилання
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