Advertisement

d-actions on compact abelian groups

  • Klaus Schmidt
Chapter
Part of the Progress in Mathematics book series (PM, volume 128)

Abstract

According to Theorem 4.2, ℤ d is of Markov type for every d ≥ 1, and ℤ d -actions by automorphisms of compact groups enjoy the properties described in (4.10), Propositions 4.9-4.10, Remark 4.15, and Theorem 4.11. Just as compact, abelian groups like T n = ℝ n /ℤ n have automorphisms with very intricate dynamical properties, there is an abundance of examples of interesting ℤ d -actions by automorphisms of compact abelian groups. In this section we introduce a general formalism for the investigation of such actions which will also give us a systematic approach to constructing actions with specified properties.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Birkhäuser Verlag 1995

Authors and Affiliations

  • Klaus Schmidt
    • 1
  1. 1.Mathematisches InstitutUniversität WienViennaAustria

Personalised recommendations