Generic properties of continuous iterated function systems with place dependent probabilities

• Autorzy: Bielaczyc T.
• Języki publikacji: EN

Abstrakty

EN

It is shown that for a typical continuous learning system denned on a compact convex subset of R[sup]n the Hausdorff dimension of its invariant measure is equal to zero.

Słowa kluczowe

EN

Markov operators; iterated function systems; Hausdorff dimension

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2007
• Tom: Vol. 55, no 1
• Strony: 81--96
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Bielaczyc T.

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

Bibliografia

• [1] T. Bielaczyc, Generic properties of iterated function systems with place dependent probabilities, Univ. lagel. Acta Math. 44 (2006), 35-46.
• [2] R. M. Dudley, Probabilities and Metrics, Aarhus Universitet, 1976.
• [3] P. Janoska, Stability of a countable iterated function system, Univ. lagel. Acta Math. 32 (1995), 105-119.
• [4] A. Lasota and M. C. Mackey, Cell division and the stability of cellular populations, J. Math. Biol. 38 (1999), 241-261.
• [5] A. Lasota and J. Myjak, Generic properties of fractal measures, Bull. Polish Acad. Sci. Math. 42 (1994), 283-296.
• [6] A. Lasota and J. A. Yorke, Lower bound technique for Markov operators and iterated function systems, Random. Comput. Dynam. 2 (1994), 41-77.
• [7] T. Szarek, Generic properties of continuous iterated function systems, Bull. Polish Acad. Sci. Math. 57 (1999), 77-89.
• [8] —, Generic properties of learning systems, Ann. Polon. Math. 73 (2000), 93-102.
• [9] —, Iterated function systems depending on a previous transformation, Univ. lagel. Acta Math. 33 (1996), 161-172.
• [10] —, On typical Markov operators acting on Borel measures, Abstr. Appl. Anal. 5 (2005), 489-497.
• [11] —, The stability of Markov operators on Polish spaces, Studia Math. 143 (2000), 145-152.