Fixed points of Lyapunov integral operators and Gibbs measures

2017/08/23 by F. H. Haydarov, Haydarov, F. H.
Mathematics · Physics and Astronomy · #FOS: Mathematics #Functional Analysis (math.FA) #Markov Chains and Monte Carlo Methods #Mathematical Dynamics and Fractals #Theoretical and Computational Physics #math.FA

paper · pdf · doi:10.48550/arxiv.1708.06902

arxiv created 2017/08/23 · openalex publication_date 2017/08/23 · arxiv updated 2017/08/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we shall consider the connections between Lyapunov integral operators and Gibbs measures for four competing interactions of models with uncountable (i.e. [0,1]) set of spin values on a Cayley tree. And we shall prove the existence of fixed points of Lyapunov integral operators and give a condition of uniqueness of fixed points.

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