## Map of fixed points and Lyapunov functions for one class of discrete dynamical systems.(English. Russian original)Zbl 0838.93062

Math. Notes 56, No. 5, 1125-1131 (1994); translation from Mat. Zametki 56, No. 5, 40-49 (1994).
The author considers a discrete dynamical system on a simplex in $$\mathbb{R}^n$$. By the use of the set of stationary points, he constructs a non trivial Lyapunov function which provides information on the set of limit points.

### MSC:

 93D30 Lyapunov and storage functions 37B99 Topological dynamics

### Keywords:

discrete dynamical system; Lyapunov function; limit points
Full Text:

### References:

 [1] R. N. Ganikhodzhaev, ”Quadratic stochastic operators, Lyapunov functions, and tournaments,”Mat. Sb.,183, No. 8, 119–140 (1992). · Zbl 0766.47037 [2] R. Horn and C. Johnson,Matrix Analysis [Russian translation], Mir, Moscow (1989). [3] F. Harary,Graph Theory [Russian translation], Mir, Moscow (1973). [4] G. Hardy, D. E. Littlewood, and G. Polya,Inequalities [Russian translation], Inostr. Lit., Moscow (1948). [5] G. Polya and G. Szegö,Problems and Theorems in Analysis, Vol. 1, Springer-Verlag, Berlin (1976). · Zbl 0311.00002
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.