The stability of fixed points of discrete dynamical systems in the space conv \(\mathbb{R}^n\). (English. Russian original) Zbl 1376.37056
Funct. Anal. Appl. 50, No. 2, 163-165 (2016); translation from Funkts. Anal. Prilozh. 50, No. 2, 94-96 (2016).
Summary: Conditions for the asymptotic Lyapunov stability of the fixed points of discrete dynamical systems in the space conv \(\mathbb{R}^n\) are established.
MSC:
| 37C25 | Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics |
| 37C75 | Stability theory for smooth dynamical systems |
| 52A20 | Convex sets in \(n\) dimensions (including convex hypersurfaces) |
References:
| [1] | Ovseevich, A. I., No article title, Funkts. Anal. Prilozhen., 44, 74-81 (2010) · doi:10.4213/faa2985 |
| [2] | Gnana Bhaskar, T.; Shaw, M., No article title, Dynam. Systems Appl., 13, 479-485 (2004) · Zbl 1073.39003 |
| [3] | Aleksandrov, A. D., No article title, Mat. Sb., 2, 947-972 (1937) · JFM 63.1234.04 |
| [4] | Y. L. Daletskii and M. G. Krein, Stability of Solutions of Differential Equations in Banach Space [in Russian], Nauka, Moscow, 1970. · Zbl 0233.34001 |
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