Continuous Iterated Function Systems on Polish spaces

• Autorzy: Horbacz, K. , Szarek, T.
• Języki publikacji: EN

Abstrakty

EN

Continuous Iterated Function Systems are studied. We generalize results proved by A. Lasota and RM. C. Mackey to the case when the systems are defined on Polish spaces.

Słowa kluczowe

PL

miara niezmiennicza; operator Markowa

EN

invariant measure; iterated function system; Markov operator

• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2001
• Tom: Vol. 49, no 2
• Strony: 191--202
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Horbacz, K.

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

autor

Szarek, T.

• Department of Mathematics, Technical University of Rzeszów, W. Pola 6, 35-959 Rzeszów, Poland

Bibliografia

• [1] P. Billingsley, Convergence of probability measures, John Wiley, New York 1968.
• [2] R. M. Dudley, Probabilities and matrics, Aarhus Universitet, Aarhus 1976.
• [3] R. Fortet, B. Mourier, Convergence de la répartition empirique vers la répartition théorétique, Ann. Sci. Ecole. Norm. Sup., 70 (1953) 267-285.
• [4] K. Horbacz, T. Szarek, Randomly connected dynamical systems on Banach spaces, Stochastic Anal. Appl., (2001), to be published.
• [5] A. Lasota, Prom fractals to stochastic differential equations, in: Chaos - the interplay between stochastic and deterministic behaviour, (Karpacz 1995), Springer-Verlag, Berlin 1995.
• [6] A. Lasota, M. C. Mackey, Cell division and the stability of cellular population, J. Math. Biol., 38 (1999) 241-261.
• [7] A. Lasota, M. C. Mackey, Chaos, Fractals and Noise - Stochastic Aspect of Dynamics, Springer-Verlag, New York 1994.
• [8] A. Lasota, J. A. Yorke, Lower bound technique for Markov operators and iterated function systems, Random Comput. Dynam., 2 (1994) 41-77.
• [9] T. Szarek, Generic properties of continuous iterated function systems, Bull. Pol. Ac.: Math., 47 (1999) 77-89.
• [10] T. Szarek, Iterated function systems with place dependent probabilities on Polish spaces, Israel J. Math., to be published.
• [11] T. Szarek, Markov operators acting on Polish spaces, Ann. Polon. Math., 67 (1997) 247-257.