Skip to main content
Log in

Numbertheoretical endomorphisms with σ-finite invariant measure

  • Published:
Israel Journal of Mathematics Aims and scope Submit manuscript

Abstract

A class of measurable transformations which serves as a model for severalf-expansions is discussed. Sufficient conditions for ergodicity and the existence of a σ-finite invariant measure are given.

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

Access this article

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. R. L. Adler,F-expansions revisted, inRecent Advances in Topological Dynamics Lecture Notes in Mathematics318 (1973), 1–5.

  2. R. L. Adler and B. Weiss,The ergodic infinite measure preserving transformation of Boole, Israel J. Math.16 (1973), 263–278.

    Article  MathSciNet  Google Scholar 

  3. H. Cohn,Support polygons and the resolution of modular functional singularities, Acta Arith.24 (1973), 261–278.

    MATH  MathSciNet  Google Scholar 

  4. R. Fischer,Ergodische Theorie von Ziffernentwicklungen in Wahrscheinlichkeitsräumen, Math. Z.128 (1972), 217–230.

    Article  MATH  MathSciNet  Google Scholar 

  5. N. A. Friedman,Introduction to Ergodic Theory, Van Nostrand-Reinhold Co., 1970.

  6. F. Hirzebruch,Über vierdimensionale Riemannsche Flächen mehrdeutiger analytischer Funktionen von zwei komplexen Veränderlichen, Math. Ann.126 (1953), 1–22.

    Article  MATH  MathSciNet  Google Scholar 

  7. A. Rényi,Representations for real numbers and their ergodic properties, Acta Math. Acad. Sci. Hungar.8 (1957), 477–493.

    Article  MATH  MathSciNet  Google Scholar 

  8. S. Rudolfer,Ergodic properties of linear fractional transformations modone, Proc. London Math. Soc. (3)23 (1971), 515–531.

    Article  MATH  MathSciNet  Google Scholar 

  9. F. Schweiger,Metrische Theorie einer Klasse zahlentheoretischer Transformationen, Acta Arith.15 (1968), 1–18, and16 (1969), 217–219.

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Schweiger, F. Numbertheoretical endomorphisms with σ-finite invariant measure. Israel J. Math. 21, 308–318 (1975). https://doi.org/10.1007/BF02757992

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02757992

Keywords

Navigation