Article

Dynamical systems of quadratic operators on set of idempotent measures

I. T. JuraevNamangan State University, Boburshox str. 161, 160107, Namangan, UzbekistanU. A. RozikovKarshi State University, Kuchabag str. 17 180119, Karshi, Uzbekistan

Ufimskii Matematicheskii Zhurnaljournal2025en

ABI

Abstract

We consider quadratic operators, which map the $n$ - dimensional simplex of idempotent measures into itself. We introduce the concept of Volterra quadratic operator on the simplex of idempotent measures and provide some general properties of such operators. We also consdier a special Volterra quadratic operator and provide a comprehensive analysis of the dynamical system generated by this operator. Moreover, the dynamical systems generated by general Volterra operators defined on 2 and 3 - dimensional simplices of idempotent measures are studied. For each case, we find fixed points and limits of trajectories.

Topics

advanced mathematical theories Mathematical Analysis and Transform Methods Spectral Theory in Mathematical Physics

Identifiers

DOI: 10.13108/2025-17-3-121

Citations and references

Cited by 017 references

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