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Morphisms of discrete dynamical systems

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  • The purpose of this paper is to introduce a category whose objects are discrete dynamical systems $( X,P,H,\theta ) $ in the sense of [6] and whose arrows will be defined starting from the notion of groupoid morphism given in [10]. We shall also construct a contravariant functor $( X,P,H,\theta ) \rightarrow $C* $( X,P,H,\theta ) $ from the subcategory of discrete dynamical systems for which $PP^{-1}$ is amenable to the category of C* -algebras, where C* $( X,P,H,\theta ) $ is the C* -algebra associated to the groupoid $G( X,P,H,\theta)$.
    Mathematics Subject Classification: Primary: 22A22, 43A22; Secondary: 46M15, 46L99, 37B99.


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