Tournaments of Volterra type transversal operators acting in a simplex Sm−1

Abstract

In the paper, we introduce the notion of transversality for Volterra quadratic stochastic operators acting in a finite- dimensional simplex Sm−1 as the positivity condition of all principal minors of an even order of a skew-symmetric matrix A = (aki). We also study a number of properties of transversal operators that are necessary for further research. One can easily note that this definition is equivalent to the classical definition of the transversality of smooth mappings. Further, we also consider the properties of the fixed points charts of transversal operators.

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DOI

10.1063/5.0057303

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