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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA


Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania


Quadratic Operators Defined on a Finite-dimensional Simplex of Idempotent Measures

Discontinuity, Nonlinearity, and Complexity 8(3) (2019) 279--286 | DOI:10.5890/DNC.2019.09.004

I. T. Juraev, M.M. Karimov

Department of Mathematics, Namangan State University, 316, Uychi st. Namangan, Uzbekistan

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We describe some quadratic operators which map the (n−1) - dimensional simplex of idempotent measures to itself. Such operators are divided to two classes: the first class contains all n×n×n - cubic matrices with nonpositive entries which in each n×n dimensional k-th matrix contains exactly one non-zero row and exactly one non-zero column; the second class contains all n×n×n - cubicmatrices with non-positive entries which has at least one quadratic zero-matrix. These matrices play a role of the stochastic matrices in the case of idempotent measures. For both classes of quadratic maps we find fixed points.


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