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Lyapunov operator L with degenerate kernel and Gibbs measures

https://doi.org/10.17586/22208054201785553558

Abstract

In this paper, we studied the fixed points of the Lyapunov operator with degenerate kernel, in which each fixed point of the operator is corresponds to a translationinvariant Gibbs measure with four competing interactions of models with uncountable set of spin values on the Cayley tree of order two. Also, it was proved that Lyapunov operator with degenerate kernel has at most three positive fixed points.

About the Authors

Yu. Kh. Eshkabilov
Karshi State University
Uzbekistan

Kashkadarya



F. H. Haydarov
National University of Uzbekistan
Uzbekistan

Tashkent



References

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For citations:


Eshkabilov Yu.Kh., Haydarov F.H. Lyapunov operator L with degenerate kernel and Gibbs measures. Nanosystems: Physics, Chemistry, Mathematics. 2017;8(5):553–558. https://doi.org/10.17586/22208054201785553558

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ISSN 2220-8054 (Print)
ISSN 2305-7971 (Online)