Geodesic
Dynamical Properties of Quadratic Homeomorphisms of a Finite-Dimensional Simplex
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference «Problems of Modern Topology and its Applications», Tome 144 (2018), pp. 104-108.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we describe the class of all quadratic homeomorphisms of a finite-dimensional simplex and examine the asymptotic behavior of positive and negative trajectories of such homeomorphisms.
Keywords: quadratic Lotka–Volterra mapping, tournament, Lyapunov functions, fixed-point chart.
Mots-clés : simplex 
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R. N. Ganikhodzhaev; M. A. Tadjieva; D. B. Èshmamatova. Dynamical Properties of Quadratic Homeomorphisms of a Finite-Dimensional Simplex. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference «Problems of Modern Topology and its Applications», Tome 144 (2018), pp. 104-108. http://geodesic.mathdoc.fr/item/INTO_2018_144_a11/

[1] Kantorovich L. V., Akilov G. P., Funktsionalnoi analiz, Nauka, M., 1977

[2] Lyubich Yu. I., Matematicheskie struktury v populyatsionnoi genetike, Nauka, M., 1984 | MR

[3] Kharari F., Teoriya grafov, 1973

[4] Ganikhodzhaev N., Ganikhodzhaev R., Jamilov U., “Quadratic stochastic operators and zero-sym game dynamics”, Ergodic Theory. Dynam. Syst., 35:5 (2015), 1443–1473 | DOI | MR

[5] Ganikhodzhaev R., Mukhamedov F., Rozikov U., “Quadratic stochastic operators and processes: Results and open problems”, Inf. Dimens. Anal. Quantum Probab. Rel. Topics, 14:2 (2011), 279–335 | DOI | MR | Zbl