Iterations of continuous mappings on metric spaces Asymptotic stability and Lyapunov functions
- 31 July 1979
- journal article
- research article
- Published by Taylor & Francis in International Journal of Systems Science
- Vol. 10 (8), 855-862
- https://doi.org/10.1080/00207727908941626
Abstract
The stability of difference equations, which represent discrete-time motions, is studied on general metric spaces. An analogous theorem to the equivalence between the asymptotic stability of invariant sets and the existence of Lyapunov functions for continuous-time motions is proved. One result is the reduction of the asymptotic stability to an invariance condition.Keywords
This publication has 12 references indexed in Scilit:
- Theories of Populations in Biological CommunitiesPublished by Springer Nature ,1977
- A Characterization of Local Convergence for Fixed Point Iterations in $R^1 $SIAM Journal on Numerical Analysis, 1975
- Biological populations obeying difference equations: Stable points, stable cycles, and chaosJournal of Theoretical Biology, 1975
- Stability of Difference Equations and Convergence of Iterative ProcessesSIAM Journal on Numerical Analysis, 1973
- Stability of non-linear discrete-time systemsInternational Journal of Control, 1973
- Some Stability Theorems for Ordinary Difference EquationsSIAM Journal on Numerical Analysis, 1967
- Concerning the convergence of iterates to fixed pointsStudia Mathematica, 1966
- Über die Anwendung der Methode von Ljapunov auf DifferenzengleichungenMathematische Annalen, 1958
- On Iteration of Mappings of a Metric Space Onto ItselfJournal of the London Mathematical Society, 1951
- On the iteration of a continuous mapping of a compact space into itselfMathematical Proceedings of the Cambridge Philosophical Society, 1950