Orbit Complexity and Entropy for Group Endomorphisms

  • Authors:

  • Robert Kenny

  • Affiliations:

  • The University of Western Australia, School of Mathematics and Statistics (M019), 35 Stirling Highway, Crawley 6009, Western Australia

  • Venue:
  • Electronic Notes in Theoretical Computer Science (ENTCS)
  • Year:
  • 2005

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Abstract

We consider the pointwise inequality (orbit complexity @? topological entropy), known in the case of computable maps and computable metric spaces, for endomorphisms of locally compact groups with an arbitrary upper semicomputable distance. Weaker conditions on the effectiveness of the product and metric neighbourhoods are observed which, in R^n, are transferred to a norm-induced metric and used to prove a version of the inequality on locally compact abelian groups.