Skip to main content
Log in

A note on periodic points for ergodic toral automorphisms

  • Published:
Monatshefte für Mathematik Aims and scope Submit manuscript

Abstract

We prove that the periodic point measures are dense in the space or invariant measures for ergodic toral automorphisms.

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. Berg, K.: Convolution of invariant measures, maximal entropy. Math. Syst. Th.3, 146–150 (1969).

    Google Scholar 

  2. Bowen, R.: Entropy expansive maps. Trans. Amer. Math. Soc.164, 323–331 (1972).

    Google Scholar 

  3. Denker, M., C. Grillenberger, andK. Sigmund: Ergodic Theory on Compact Spaces. Lecture Notes Math. 527. Berlin-Heidelberg-New York: Springer. 1978.

    Google Scholar 

  4. Hirsch, M., andC. Pugh: Stable manifolds for hyperbolic sets. Proc. Symp. Pure Math. V, p. 14. Providence, R. I.: Amer. Math. Soc. 1970.

    Google Scholar 

  5. Hirsch, M., andS. Smale: Differential Equations, Dynamical Systems and Linear Algebra. New York-London: Academic Press. 1974.

    Google Scholar 

  6. Lind, D.: The structure of skew products with ergodic group automorphisms. Israel J. Math.28, 205–248 (1977).

    Google Scholar 

  7. Lind, D.: Split skew products, a related functional equation and specification. Israel J. Math.30, 236–254 (1978).

    Google Scholar 

  8. Lind, D.: Ergodic group automorphisms and specification. Proc. Ergodic Theory Conf. Oberwolfach. Lecture Note Math. (To appear.)

  9. Miles, G., andK. Thomas: On the polynomial uniformity of translations of then-torus. Studies in Ergodic Theory and Probability, vol. 2, pp. 219–230. New York: Academic Press.

  10. Miles, G., andK. Thomas: Generalized torus automorphisms are Bernoulli. Studies in Ergodic Theory and Probability, vol. 2, pp. 231–250. New York: Academic Press.

  11. Sigmund, K.: Generic properties of invariant measure for axiomA diffeomorphisms. Invent. Math.11, 99–109 (1970).

    Google Scholar 

  12. Sigmund, K.: On dynamical systems with the specification property. Trans. Amer. Math. Soc.190, 285–299 (1974).

    Google Scholar 

  13. Stolarsky, K.: Algebraic Numbers and Diophantine Approximation. New York: Marcel Dekker. 1974.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Marcus, B. A note on periodic points for ergodic toral automorphisms. Monatshefte für Mathematik 89, 121–129 (1980). https://doi.org/10.1007/BF01476590

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01476590

Keywords

Navigation