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

show all references

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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