# American Institute of Mathematical Sciences

January  2011, 29(1): 91-107. doi: 10.3934/dcds.2011.29.91

## Morphisms of discrete dynamical systems

 1 University Constantin Brăncuşi of Tărgu-Jiu, Str. Geneva, Nr. 3, 210136 Tărgu-Jiu, Romania

Received  February 2010 Revised  June 2010 Published  September 2010

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 $G( X,P,H,\theta)$.
Citation: Mădălina Roxana Buneci. Morphisms of discrete dynamical systems. Discrete & Continuous Dynamical Systems - A, 2011, 29 (1) : 91-107. doi: 10.3934/dcds.2011.29.91
##### References:
 [1] C. Anantharaman-Delaroche and J. Renault, "Amenable groupoids,", Monographie de L'Enseignement Mathematique No 36, 36 (2000). Google Scholar [2] M. Buneci, Groupoid C*-algebras,, Surveys in Mathematics and its Applications, 1 (2006), 71. Google Scholar [3] M. Buneci, A category of singly generated dynamical systems,, in, (2007), 122. Google Scholar [4] M. Buneci, Groupoid categories,, in, 8 (2008), 27. Google Scholar [5] M. Buneci and P. Stachura, Morphisms of locally compact groupoids endowed with Haar systems,, , (). Google Scholar [6] R. Exel and J. Renault, Semigroups of local homeomorphisms and interaction groups,, Ergodic Theory Dynam. Systems, 27 (2007), 1737. doi: doi:10.1017/S0143385707000193. Google Scholar [7] P. Muhly, J. Reanult and D. Williams, Equivalence and isomorphism for groupoid C*-algebras,, J. Operator Theory, 17 (1987), 3. Google Scholar [8] J. Renault, "A Groupoid Approach to C*- algebras,", Lecture Notes in Math. Springer-Verlag, 793 (1980). Google Scholar [9] S. L. Woronowicz, Pseudospaces, pseudogroups and Pontrjagin duality,, in, 116 (1979). Google Scholar [10] S. Zakrzewski, Quantum and classical pseudogroups I,, Comm. Math. Phys., 134 (1990), 347. doi: doi:10.1007/BF02097706. Google Scholar

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##### References:
 [1] C. Anantharaman-Delaroche and J. Renault, "Amenable groupoids,", Monographie de L'Enseignement Mathematique No 36, 36 (2000). Google Scholar [2] M. Buneci, Groupoid C*-algebras,, Surveys in Mathematics and its Applications, 1 (2006), 71. Google Scholar [3] M. Buneci, A category of singly generated dynamical systems,, in, (2007), 122. Google Scholar [4] M. Buneci, Groupoid categories,, in, 8 (2008), 27. Google Scholar [5] M. Buneci and P. Stachura, Morphisms of locally compact groupoids endowed with Haar systems,, , (). Google Scholar [6] R. Exel and J. Renault, Semigroups of local homeomorphisms and interaction groups,, Ergodic Theory Dynam. Systems, 27 (2007), 1737. doi: doi:10.1017/S0143385707000193. Google Scholar [7] P. Muhly, J. Reanult and D. Williams, Equivalence and isomorphism for groupoid C*-algebras,, J. Operator Theory, 17 (1987), 3. Google Scholar [8] J. Renault, "A Groupoid Approach to C*- algebras,", Lecture Notes in Math. Springer-Verlag, 793 (1980). Google Scholar [9] S. L. Woronowicz, Pseudospaces, pseudogroups and Pontrjagin duality,, in, 116 (1979). Google Scholar [10] S. Zakrzewski, Quantum and classical pseudogroups I,, Comm. Math. Phys., 134 (1990), 347. doi: doi:10.1007/BF02097706. Google Scholar
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