Positive fixed points of cubic operators on ℝ² and Gibbs Measures

2018/12/19 by Yu. Kh. Èshkabilov, Yu. Kh. Eshkabilov, Eshkabilov, Yu. Kh. +2
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Functional Equations Stability Results #Mathematical Dynamics and Fractals #Mathematical and Theoretical Analysis #math.FA

paper · pdf · doi:10.48550/arxiv.1812.07744

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openalex publication_date 2018/12/19 · arxiv created 2019/03/18 · arxiv updated 2019/03/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we consider one model with nearest-neighbor interactions and with the set [0,1] of spin values on the Cayley tree of order three. Translation-invariant Gibbs measures for the model are studied. Results are proved by using properties of the positive fixed points of a cubic operator in the cone ℝ₊².

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