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arXiv · 0712.2891

On homotopy of volterrian quadratic stochastic operators

Farrukh Mukhamedov·Mansoor Saburov
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Abstract

In the present paper we introduce a notion of homotopy of two Volterra operators which is related to fixed points of such operators. It is establish a criterion when two Volterra operators are homotopic, as a consequence we obtain that the corresponding tournaments of that operators are the same. This, due to \cite{Ga1}, gives us a possibility to know some information about the trajectory of homotopic Volterra operators. Moreover, it is shown that any Volterra q.s.o. given on a face has at least two homotopic extension to the whole simplex.

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Farrukh Mukhamedov, Mansoor Saburov. 2007-12-18. On homotopy of volterrian quadratic stochastic operators. https://arxiv.org/abs/0712.2891

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