English

Lyapunov operator $\mathcal L$ with degenerate kernel and Gibbs measures

Functional Analysis 2017-08-24 v1

Abstract

In this paper we'll give a connection between four competing interactions (external field, nearest neighbor, second neighbors and triples of neighbors) of models with uncountable (i.e. [0,1][0,1]) set of spin values on the Cayley tree of order two and Lyapunov integral equation. Also we'll study fixed points of Lyapunov operator with degenerate kernel which each fixed point of the operator is correspond to a {\it translation-invariant} Gibbs measure.

Keywords

Cite

@article{arxiv.1708.06903,
  title  = {Lyapunov operator $\mathcal L$ with degenerate kernel and Gibbs measures},
  author = {Yu. Kh. Eshkabilov and F. H. Haydarov},
  journal= {arXiv preprint arXiv:1708.06903},
  year   = {2017}
}

Comments

arXiv admin note: text overlap with arXiv:1509.04883