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  1. ; (, Transactions of the American Mathematical Society)
    Building on work of Ruelle and Putnam in the Smale space case, Thomsen defined the homoclinic and heteroclinic -algebras for an expansive dynamical system. In this paper we define a class of expansive dynamical systems, called synchronizing dynamical systems, that exhibit hyperbolic behavior almost everywhere. Synchronizing dynamical systems generalize Smale spaces (and even finitely presented systems). Yet they still have desirable dynamical properties such as having a dense set of periodic points. We study various -algebras associated with a synchronizing dynamical system. Among other results, we show that the homoclinic algebra of a synchronizing system contains an ideal which behaves like the homoclinic algebra of a Smale space. 
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  2. ; ; (, Mathematische Annalen)
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  3. (, Ergodic Theory and Dynamical Systems)
    Abstract Scarparo has constructed counterexamples to Matui’s HK-conjecture. These counterexamples and other known counterexamples are essentially principal but not principal. In the present paper, a counterexample to the HK-conjecture that is principal is given. Like Scarparo’s original counterexample, our counterexample is the transformation groupoid associated to a particular odometer. However, the relevant group is the fundamental group of a flat manifold (and hence is torsion-free) and the associated odometer action is free. The examples discussed here do satisfy the rational version of the HK-conjecture. 
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  4. ; ; (, Groups, Geometry, and Dynamics)
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  5. ; ; ; ; ; ; ; ; ; (, Münster journal of mathematics)
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  6. ; ; (, Proceedings of the American Mathematical Society)
    Examples of Fell algebras with compact spectrum and trivial Dixmier-Douady invariant are constructed to illustrate differences with the case of continuous-trace C ∗ C^* -algebras. At the level of the spectrum, this translates to only assuming the spectrum is locally Hausdorff (rather than Hausdorff). The existence of (full) projections is the fundamental question considered. The class of Fell algebras studied here arises naturally in the study of Wieler solenoids and applications to dynamical systems will be discussed in a separate paper. 
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  7. ; ; (, Proceedings of the American Mathematical Society)
    Floyd gave an example of a minimal dynamical system which was an extension of an odometer and the fibres of the associated factor map were either singletons or intervals. Gjerde and Johansen showed that the odometer could be replaced by any Cantor minimal system. Here, we show further that the intervals can be generalized to cubes of arbitrary dimension and to attractors of certain iterated function systems. We discuss applications. 
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