Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences
Abstract
In this paper it is found fixed points of Lyapunov integral equation and considered the connections between Gibbs measures for four competing interactions of models with uncountable (i.e. $[0,1]$) set of spin values on the Cayley tree of order two.
First Page
19
Last Page
23
References
1. Eshkabilov Yu. Kh, Haydarov F. H., Rozikov U. A. Uniqueness of Gibbs measure for models with uncountable set of spin values on a Cayley tree. Math. Phys. Anal. Geom., 2013, V.16, pp.1–17.
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4. Nirenberg L. Topics in nonlinear functional analysis. AMS, Courant Lec. Notes in Math, 6, N.Y., 2001. – 145 p.
5. Rozikov U. A., Haydarov F. H. Four competing interactions for models with an uncountable set of spin values on a Cayley tree. Theor. Math. Phys., 2017, V. 191, No. 3, pp.910–923.
6. Rozikov U. A. Gibbs measures on Cayley trees. World Scientific, 2013. – 404 p.
Recommended Citation
Haydarov, Farkhod
(2018)
"Positive fixed points of Lyapunov integral operators and Gibbs measures,"
Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences: Vol. 1:
Iss.
1, Article 9.
DOI: https://doi.org/10.56017/2181-1318.1008