Resolving Extensions of Finitely Presented Systems

  • Authors:

  • Todd Fisher

  • Affiliations:

  • Department of Mathematics, Brigham Young University, Provo, USA 84602

  • Venue:
  • Acta Applicandae Mathematicae: an international survey journal on applying mathematics and mathematical applications
  • Year:
  • 2013

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Abstract

In this paper we extend certain central results of zero dimensional systems to higher dimensions. The first main result shows that if (Y,f) is a finitely presented system, then there exists a Smale space (X,F) and a u-resolving factor map 驴 +:X驴Y. If the finitely presented system is transitive, then we show there is a canonical minimal u-resolving Smale space extension. Additionally, we show that any finite-to-one factor map between transitive finitely presented systems lifts through u-resolving maps to an s-resolving map.