Skip to main content
SpringerLink
Log in

The genesis of the notion of distributional chaos

  • Conferenze
  • Published:
Rendiconti del Seminario Matematico e Fisico di Milano Aims and scope Submit manuscript

Abstract

The purpose of this paper is to indicate how the theory of distributional chaos was motivated by certain constructs from the theory of probabilistic metric spaces, to introduce the notion of distributional chaos and to illustrate some of its features with a simple example.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Balibrea, F., Schweizer, B., Sklar, A. andSmítal, J.,Generalized specification property and distributional chaos, to appear.

  2. Erber, T., Rynne, T.M., Darsow, W.F. andFrank, M.J.,The simulation of random processes on digital computers: unavoidable order, Journal of Computational Physics,49 (1983), 394–419.

    Article  MATH  MathSciNet  Google Scholar 

  3. Erber, T., Schweizer, B. andSklar, A.,Mixing transformations on metric spaces, Comm. Math. Phys.,29 (1973), 311–317.

    Article  MATH  MathSciNet  Google Scholar 

  4. Forti, G.L., Paganoni, L. andSmítal, J.,Strange triangular maps of the square, Bull. Austral. Math. Soc.,51 (1995), 395–415.

    Article  MATH  MathSciNet  Google Scholar 

  5. Forti, G.L. andPaganoni, L.,A distributionally chaotic triangular map with zero sequence topological entropy, Mathematica Pannonica, to appear.

  6. Johnson, P. andSklar, A.,Recurrence and dispersion under iteration of Cěbyšev polynomials, J. Math. Anal. Appl.,54 (1976), 752–771.

    Article  MATH  MathSciNet  Google Scholar 

  7. Schweizer, B. andSklar, A.,Probabilistic metric spaces determined by measure-preserving transformations, Z. Wahrsch. Verw. Geb.,26 (1973), 235–239.

    Article  MATH  MathSciNet  Google Scholar 

  8. Schweizer, B. andSklar, A., Probabilistic Metric Spaces, Elsevier North-Holland, 1983.

    MATH  Google Scholar 

  9. Schweizer, B. andSmítal, J.,Measures of chaos and a spectral decomposition of dynamical systems on the interval, Trans. Amer. Math. Soc.,344 (1994), 737–754.

    Article  MATH  MathSciNet  Google Scholar 

  10. Schweizer, B., Sklar, A. andSmítal, J.,Distributional (and other) chaos and its measurement, to appear.

  11. Sherwood, H.,A note on PM spaces determined by measure preserving transformations, Z. Wahrsch. Verw. Geb.,33 (1976), 353–354.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Massachusetts, 01003, Amherst, MA, U.S.A.

    Berthold Schweizer

Authors
  1. Berthold Schweizer
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Conferenza tenuta il 23 maggio 1996

Rights and permissions

Reprints and permissions

About this article

Cite this article

Schweizer, B. The genesis of the notion of distributional chaos. Seminario Mat. e. Fis. di Milano 66, 159–167 (1996). https://doi.org/10.1007/BF02925359

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02925359

Keywords

Search

Navigation