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Smallness and Comparison Properties for Minimal Dynamical Systems

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arxiv 1306.6681 v1 pith:2T5AKMYV submitted 2013-06-27 math.DS math.OA

Julian Buck This is my paper · ORCID
classification math.DSmath.OA
keywords systemscomparisondynamicalminimalpropertyalgebrasapplicationsclass
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We introduce the dynamic comparison property for minimal dynamical systems which has applications to the study of crossed product C*-algebras. We demonstrate that this property holds for a large class of systems which includes all examples where the underlying space is finite-dimensional, as well as for an explicit infinite-dimensional example, showing that the it is strictly weaker than finite-dimensionality in general.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Dynamical comparison for local homeomorphisms

    math.OA 2026-08 conditional novelty 8.0 of 10

    Minimal surjective local homeomorphisms of finite-dimensional compact spaces give Deaconu-Renault groupoids with dynamical comparison, yielding UCT Kirchberg algebras and, in the Cantor case, Matui's AH conjecture.

  2. Topologically free minimal actions without dynamical comparison

    math.DS 2026-07 unverdicted novelty 7.0 of 10

    Existence of topologically free minimal F_∞-actions on the Cantor set without dynamical comparison (with or without invariant measures), plus separation of strict comparison in the crossed product from dynamical compa...

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