Invariant measures for iterated function systems

• Autorzy: Tomasz Szarek
• Języki publikacji: EN

Abstrakty

EN

A new criterion for the existence of an invariant distribution for Markov operators is presented. Moreover, it is also shown that the unique invariant distribution of an iterated function system is singular with respect to the Hausdorff measure.

Słowa kluczowe

EN

Markov operator; invariant measure; iterated function system

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2000
• Tom: 75
• Numer: 1
• Strony: 87-98

Daty

wydano

2000

otrzymano

2000-02-28

poprawiono

2000-05-28

Twórcy

autor

Tomasz Szarek

• Institute of Mathematics, Polish Academy of Sciences, Bankowa 14, 40-007 Katowice, Poland

Bibliografia

• [1] Arbeiter M. and Patzschke N., Random self-similar multifractals, Math. Nachr. 181 (1996), 5-42.
• [2] Dudley R. M., Probabilities and Matrices, Aarhus Universitet, 1976.
• [3] Falconer K. J., Fractal Geometry: Mathematical Foundations and Applications, Wiley, New York, 1990.
• [4] Falconer K. J. , The Geometry of Fractal Sets, Cambridge Univ. Press, Cambridge, 1985.
• [5] R. Fortet et Mourier B., Convergence de la répartition empirique vers la répartition théorétique, Ann. Sci. École Norm. Sup. 70 (1953), 267-285.
• [6] Geronimo J. S. and Hardin D. P., An exact formula for the measure dimensions associated with a class of piecewise linear maps, Constr. Approx. 5 (1989), 89-98.
• [7] Hata M., On the structure of self-similar sets, Japan J. Appl. Math. 2 (1985), 381-414.
• [8] Hutchinson J. E., Fractals and self-similarities, Indiana Univ. Math. J. 30 (1981), 713-747.
• [9] Lasota A. and Myjak J., Generic properties of fractal measures, Bull. Polish Acad. Sci. Math. 42 (1994), 283-296.
• [10] Lasota A. and Myjak J., Semifractals on Polish spaces, ibid. 46 (1998), 179-196.
• [11] Lasota A. and Yorke J. A., Lower bound technique for Markov operators and iterated function systems, Random Comput. Dynam. 2 (1994), 41-77.
• [12] Szarek T., Markov operators acting on Polish spaces, Ann. Polon. Math. 67 (1997), 247-257.