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.
Keywords
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