Dynamical systems with multiplicative perturbations: the strong convergence of measures

• Autorzy: Katarzyna Horbacz
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

dynamical system; Markov operator; strong asymptotic stability; iterated function system

Kategorie tematyczne

• 47D07: Markov semigroups and applications to diffusion processes
• 47A35: Ergodic theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1993
• Tom: 58
• Numer: 1
• Strony: 85-93

Daty

wydano

1993

otrzymano

1992-04-13

poprawiono

1992-05-18

Twórcy

autor

Katarzyna Horbacz

• Institute of Mathematics, Silesian University, Bankowa 14, 40-007 Katowice, Poland

Bibliografia

• [1] 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.
• [2] 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.
• [3] K. Horbacz, Dynamical systems with multiplicative perturbations, Ann. Polon. Math. 50 (1989), 93-102.
• [4] K. Horbacz, Asymptotic stability of dynamical systems with multiplicative perturbations, ibid. 50 (1989), 209-218.
• [5] A. Lasota and J. Tyrcha, On the strong convergence to equilibrium for randomly perturbed dynamical systems, ibid. 53 (1991), 79-89.
• [6] A. Lasota and M. C. Mackey, Stochastic perturbation of dynamical systems: The weak convergence of measures, J. Math. Anal. Appl. 138 (1989), 232-248.
• [7] A. Lasota and M. C. Mackey, Probabilistic Properties of Deterministic Systems, Cambridge Univ. Press, Cambridge 1985.
• [8] M. Podhorodyński, Stability of Markov processes, Univ. Iagell. Acta Math. 27 (1988), 285-296.