Hostname: page-component-76fb5796d-vvkck Total loading time: 0 Render date: 2024-04-29T18:26:25.839Z Has data issue: false hasContentIssue false
  • English
  • Français

Some results on the classification of expansive automorphisms of compact abelian groups

Published online by Cambridge University Press:  19 September 2008

Fabio Fagnani
Fabio Fagnani
Affiliation:
Scuola Normale Superiore, Piazza dei Cavalieri 7, 56100 Pisa, Italy
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper we study expansive automorphisms of compact 0-dimensional abelian groups. Our main result is the complete algebraic and topological classification of the transitive expansive automorpisms for which the maximal order of the elements is p2 for a prime p. This yields a classification of the transitive expansive automorphisms with topological entropy log p2. Finally, we prove a necessary and sufficient condition for an expansive automorphism to be conjugated, topologically and algebraically, to a shift over a finite group.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 16 , Issue 1 , February 1996 , pp. 45 - 50
Copyright
Copyright © Cambridge University Press 1996

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Kitchens, B. P.. Expansive dynamics on zero-dimensional groups. Ergod. Th. & Dynam. Sys. 7 (1987), 249–261.CrossRefGoogle Scholar
[2]Kitchens, B. P. and Schmidt, K.. Automorphisms of compact groups. Ergod. Th. & Dynam. Sys. 9 (1989), 691–735.CrossRefGoogle Scholar
[3]Loeliger, H.-A. and Mittelholzer, T.. Convolutional codes over groups. Preprint.Google Scholar
[4]Miles, G. and Thomas, R. K.. The breakdown of automorphisms of compact topological groups. Studies in Probability and Ergodic Theory. Rota, G. C., ed. Academic Press, New York, 1978.Google Scholar
[5]Schmidt, K.. Automorphisms of compact abelian groups and affine varieties. Proc. London Math. Soc. 61 (1990), 480–496.CrossRefGoogle Scholar
[6]Trott, M. D.. The algebraic structure of trellis codes. PhD Dissertation, Stanford University, 1992.Google Scholar
[7]Willems, J. C.. Models for dynamics. Dynamics Reported 2 (1989), 171–269.CrossRefGoogle Scholar
[8]Yuzvinskii, S. A.. Metric properties of endomorphisms of compact groups. Amer. Math. Soc. Transl. Ser. 2 66 (1986), 63–98.Google Scholar