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Creators/Authors contains: "DEELEY, ROBIN J."

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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. ; ; ; ; ; ; ; ; ; (, Münster journal of mathematics)
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