Article Contents
Article Contents

# Morphisms of discrete dynamical systems

• 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.

 Citation:

•  [1] C. Anantharaman-Delaroche and J. Renault, "Amenable groupoids," Monographie de L'Enseignement Mathematique No 36, Geneve, 2000. [2] M. Buneci, Groupoid C*-algebras, Surveys in Mathematics and its Applications, 1 (2006), 71-98. [3] M. Buneci, A category of singly generated dynamical systems, in "International Conference on Dynamical Systems" (2007), International Academic Press, 122-129. [4] M. Buneci, Groupoid categories, in "Perspectives in Operators Algebras and Mathematical Physics," 27-40, Theta Ser. Adv. Math., 8, Theta, Bucharest, 2008. [5] M. Buneci and P. Stachura, Morphisms of locally compact groupoids endowed with Haar systems, arXiv:math.OA/0511613. [6] R. Exel and J. Renault, Semigroups of local homeomorphisms and interaction groups, Ergodic Theory Dynam. Systems, 27 (2007), 1737-1771.doi: doi:10.1017/S0143385707000193. [7] P. Muhly, J. Reanult and D. Williams, Equivalence and isomorphism for groupoid C*-algebras, J. Operator Theory, 17 (1987), 3-22. [8] J. Renault, "A Groupoid Approach to C*- algebras," Lecture Notes in Math. Springer-Verlag, 793, 1980. [9] S. L. Woronowicz, Pseudospaces, pseudogroups and Pontrjagin duality, in "Proc. of the International Conference on Math. Phys.," Lausanne 1979, Lecture Notes in Math., 116. [10] S. Zakrzewski, Quantum and classical pseudogroups I, Comm. Math. Phys., 134 (1990), 347-370.doi: doi:10.1007/BF02097706.