Invariant measures for iterated function systems

Tomasz Szarek

Annales Polonici Mathematici (2000)

  • Volume: 75, Issue: 1, page 87-98
  • ISSN: 0066-2216

Abstract

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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.

How to cite

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Szarek, Tomasz. "Invariant measures for iterated function systems." Annales Polonici Mathematici 75.1 (2000): 87-98. <http://eudml.org/doc/208388>.

@article{Szarek2000,
abstract = {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.},
author = {Szarek, Tomasz},
journal = {Annales Polonici Mathematici},
keywords = {Markov operator; invariant measure; iterated function system; invariant measures; general Markov operators; Polish spaces; iterated function systems; singular with respect to Hausdorff measure},
language = {eng},
number = {1},
pages = {87-98},
title = {Invariant measures for iterated function systems},
url = {http://eudml.org/doc/208388},
volume = {75},
year = {2000},
}

TY - JOUR
AU - Szarek, Tomasz
TI - Invariant measures for iterated function systems
JO - Annales Polonici Mathematici
PY - 2000
VL - 75
IS - 1
SP - 87
EP - 98
AB - 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.
LA - eng
KW - Markov operator; invariant measure; iterated function system; invariant measures; general Markov operators; Polish spaces; iterated function systems; singular with respect to Hausdorff measure
UR - http://eudml.org/doc/208388
ER -

References

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  1. [1] Arbeiter M. and Patzschke N., Random self-similar multifractals, Math. Nachr. 181 (1996), 5-42. Zbl0873.28003
  2. [2] Dudley R. M., Probabilities and Matrices, Aarhus Universitet, 1976. Zbl0355.60004
  3. [3] Falconer K. J., Fractal Geometry: Mathematical Foundations and Applications, Wiley, New York, 1990. 
  4. [4] Falconer K. J. , The Geometry of Fractal Sets, Cambridge Univ. Press, Cambridge, 1985. Zbl0587.28004
  5. [5] R. Fortet et Mourier B., Convergence de la répartition empirique vers la répartition théorétique, Ann. Sci. École Norm. Sup. 70 (1953), 267-285. Zbl0053.09601
  6. [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. Zbl0666.28004
  7. [7] Hata M., On the structure of self-similar sets, Japan J. Appl. Math. 2 (1985), 381-414. Zbl0608.28003
  8. [8] Hutchinson J. E., Fractals and self-similarities, Indiana Univ. Math. J. 30 (1981), 713-747. Zbl0598.28011
  9. [9] Lasota A. and Myjak J., Generic properties of fractal measures, Bull. Polish Acad. Sci. Math. 42 (1994), 283-296. Zbl0851.28004
  10. [10] Lasota A. and Myjak J., Semifractals on Polish spaces, ibid. 46 (1998), 179-196. Zbl0921.28007
  11. [11] Lasota A. and Yorke J. A., Lower bound technique for Markov operators and iterated function systems, Random Comput. Dynam. 2 (1994), 41-77. Zbl0804.47033
  12. [12] Szarek T., Markov operators acting on Polish spaces, Ann. Polon. Math. 67 (1997), 247-257. Zbl0903.60052

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