ArticleOriginal scientific text
Title
Dynamical systems with multiplicative perturbations: the strong convergence of measures
Authors 1
Affiliations
- Institute of Mathematics, Silesian University, Bankowa 14, 40-007 Katowice, Poland
Abstract
We give sufficient conditions for the strong asymptotic stability of the distributions of dynamical systems with multiplicative perturbations. We apply our results to iterated function systems.
Keywords
dynamical system, Markov operator, strong asymptotic stability, iterated function system
Bibliography
- M. F. Barnsley and S. Demko, Iterated function systems and the global construction of fractals, Proc. Roy. Soc. London Ser. A 399 (1985), 243-275.
- M. F. Barnsley, V. Ervin, D. Hardin and J. Lancaster, Solution of an inverse problem for fractals and other sets, Proc. Nat. Acad. Sci. U.S.A. 83 (1986), 1975-1977.
- K. Horbacz, Dynamical systems with multiplicative perturbations, Ann. Polon. Math. 50 (1989), 93-102.
- K. Horbacz, Asymptotic stability of dynamical systems with multiplicative perturbations, ibid. 50 (1989), 209-218.
- A. Lasota and J. Tyrcha, On the strong convergence to equilibrium for randomly perturbed dynamical systems, ibid. 53 (1991), 79-89.
- A. Lasota and M. C. Mackey, Stochastic perturbation of dynamical systems: The weak convergence of measures, J. Math. Anal. Appl. 138 (1989), 232-248.
- A. Lasota and M. C. Mackey, Probabilistic Properties of Deterministic Systems, Cambridge Univ. Press, Cambridge 1985.
- M. Podhorodyński, Stability of Markov processes, Univ. Iagell. Acta Math. 27 (1988), 285-296.