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 π +:X→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.
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Acknowledgements
The author would like to thank Mike Boyle for pointing out these problems and offering helpful advice and remarks. Also, the referee for making many useful observations and suggestions.
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Dedicated to the memory of Ki Hang Kim.
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Fisher, T. Resolving Extensions of Finitely Presented Systems. Acta Appl Math 126, 131–163 (2013). https://doi.org/10.1007/s10440-013-9811-x
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DOI: https://doi.org/10.1007/s10440-013-9811-x