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Dynamical systems on a simplex of idempotent measures Jurayev Ilkhomjon Tursunmukhammedovich Namangan State University |
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Аннотация: We study quadratic operators acting on the n-dimensional simplex of idempotent measures and mapping it into itself. The notion of a Volterra quadratic operator on the simplex of idempotent measures is introduced, and several of its general properties are established. A particular class of Volterra quadratic operators is examined in detail, and a complete qualitative analysis of the dynamical system generated by such an operator is presented. Furthermore, we investigate the dynamical behavior of systems generated by general Volterra quadratic operators on the simplices of idempotent measures of dimensions two, three, and four. For each case, all fixed points are determined and the asymptotic behavior of trajectories is described. Website: https://us06web.zoom.us/j/3836418273 |
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