najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/22208054201785553558najo-593Research ArticleMATHEMATICSМАТЕМАТИКАLyapunov operator L with degenerate kernel and Gibbs measuresEshkabilovYu. Kh.

Kashkadarya

HaydarovF. H.

Tashkent

Karshi State UniversityUzbekistanNational University of UzbekistanUzbekistan20171208202585553–558Copyright © Eshkabilov Y.K., Haydarov F.H., 20252025Eshkabilov Y.K., Haydarov F.H.Eshkabilov Y.K., Haydarov F.H.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/593

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.

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The authors declare that there are no conflicts of interest present.