A class of nonergodic Lotka-Volterra operators

On the basis of some numerical calculations, Ulam has conjectured that the ergodic theorem holds for any quadratic stochastic operator acting on a finite-dimensional simplex. However, Zakharevich showed that Ulam’s conjecture is false in general. Later, Ganikhodzhaev and Zanin generalized Zakharevic...

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Veröffentlicht in:Mathematical Notes 2015-05, Vol.97 (5-6), p.759-763
1. Verfasser: Saburov, M.
Format: Artikel
Sprache:eng
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Zusammenfassung:On the basis of some numerical calculations, Ulam has conjectured that the ergodic theorem holds for any quadratic stochastic operator acting on a finite-dimensional simplex. However, Zakharevich showed that Ulam’s conjecture is false in general. Later, Ganikhodzhaev and Zanin generalized Zakharevich’s example to the class of quadratic stochastic Volterra operators acting on a 2D simplex. In this paper, we provide a class of nonergodic Lotka-Volterra operators which includes all previous operators used in this context.
ISSN:0001-4346
1573-8876
DOI:10.1134/S0001434615050107