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On homotopy of volterrian quadratic stochastic operators

Dynamical Systems 2007-12-19 v1 Functional Analysis

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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Cite

@article{arxiv.0712.2891,
  title  = {On homotopy of volterrian quadratic stochastic operators},
  author = {Farrukh Mukhamedov and Mansoor Saburov},
  journal= {arXiv preprint arXiv:0712.2891},
  year   = {2007}
}

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12 pages