Skip to main content
SpringerLink
Log in

Fractals, Multifunctions and Markov Operators

  • Conference paper
Fractals in Graz 2001

Part of the book series: Trends in Mathematics ((TM))

  • 444 Accesses

Abstract

We show that attractors of multifunctions have many properties similar to fractals and we introduce the notion of a semiattractor and a semifractal. Further we study the relationship between the multifunctions and transition functions appearing in the theory of Markov operators. We also discuss some properties of a new dimension of measures defined by a use of the Lévy concentration function.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 129.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M.F. Barnsley, Fractals Everywhere, Academic Press, New York 1993.

    MATH  Google Scholar 

  2. C. Castaing and M. Valadier, Convex Analysis and Measurable Multifunctions Lecture Notes in Math. 580, Springer Verlag, Berlin, New York 1997.

    Google Scholar 

  3. R.M. Dudley, Probabilities and Metrics, Lecture Notes, Ser., 45, Aarhus Univ., Aarhus 1978.

    Google Scholar 

  4. K.J. Falconer, Techniques in Fractal Geometry, John Viley, New York 1997.

    MATH  Google Scholar 

  5. G. Goodman, The chaos game algorithm and statistical mechanics, preprint.

    Google Scholar 

  6. W. Hengartner and R.. Theodorescu, Concentration Functions, Academic Press, New York-London, 1973.

    MATH  Google Scholar 

  7. K. Kuratowski, Topology, vol. I, Academic Press, New York 1966.

    Google Scholar 

  8. A. Lasota and M. Mackey, Chaos, Fractals and Noice, Stochastic Aspects of Dynamics, Appl. Math. Sci., 97 Springer Verlag, New York 1994.

    Google Scholar 

  9. A. Lasota and J. Myjak, Markov operators and fractals, Bull. Pol. Ac.: Math., 45 (1997), 197–210.

    MathSciNet  MATH  Google Scholar 

  10. A. Lasota and J. Myjak, Semifractals on Polish spaces, Bull. Pol. Ac.: Math., 46 (1998), 179–196.

    MathSciNet  MATH  Google Scholar 

  11. A. Lasota and J. Myjak, Attractors of multifunctions, Bull. Pol. Ac.: Math., 48 (2000), 319–334.

    MathSciNet  MATH  Google Scholar 

  12. A. Lasota and J. Myjak, On a dimension of measures, Bull. Pol. Ac.: Math., (to appear).

    Google Scholar 

  13. A. Lasota, J. Myjak and T. Szarek, Markov operators with a unique invariant measures, (to appear).

    Google Scholar 

  14. P. Mattila, Geometry of sets and Measures in Eucledean Spaces, Cambridge University Press 1995.

    Book  Google Scholar 

  15. E. Michael Continuous selections I, Ann. of Math., 62 (1956), 361–382.

    Article  MathSciNet  Google Scholar 

  16. Ya. Pesin, Dimension Theory in Dynamical Systems, Chicago Lectures in Mathematics, University of Chicago Press 1997.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, Silesian University, Institute of Mathematics Polish Academy of Sciences, Bankowa 14, 40-007, Katowice, Poland

    Andrzej Lasota

  2. Dipartimento di Matematica Pura ed Applicata, Università di L’Aquila, Via Vetoio, 67100, L’Aquila, Italy

    Józef Myjak

Authors
  1. Andrzej Lasota
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Józef Myjak
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institut für Mathematik A, Technische Universität Graz, Steyrergasse 30, 8010, Graz, Austria

    Peter Grabner

  2. Institut für Mathematik C, Technische Universität Graz, Steyrergasse 30, 8010, Graz, Austria

    Wolfgang Woess

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer Basel AG

About this paper

Cite this paper

Lasota, A., Myjak, J. (2003). Fractals, Multifunctions and Markov Operators. In: Grabner, P., Woess, W. (eds) Fractals in Graz 2001. Trends in Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8014-5_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-0348-8014-5_7

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9403-6

  • Online ISBN: 978-3-0348-8014-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation