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Periodic points

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

Abstract

As we have seen in Theorem 5.7, every ℤ d -action by automorphisms of a compact, abelian group satisfying the d.c.c. has a dense set of periodic points (Definition 5.5), and Example 5.6 (1) shows that the d.c.c. cannot be dropped in general. In this section we investigate the density of the set of periodic points for a ℤ d -action α by automorphisms of compact group X satisfying the d.c.c. We begin with two examples which show that—if X is non-abelian—the d.c.c. does not necessarily imply that the set of α-periodic points is dense.

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Copyright information

© Birkhäuser Verlag 1995

Authors and Affiliations

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

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