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).

[2]

M. Buneci, Groupoid C*-algebras,, Surveys in Mathematics and its Applications, 1 (2006), 71.

[3]

M. Buneci, A category of singly generated dynamical systems,, in, (2007), 122.

[4]

M. Buneci, Groupoid categories,, in, 8 (2008), 27.

[5]

M. Buneci and P. Stachura, Morphisms of locally compact groupoids endowed with Haar systems,, , ().

[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.

[7]

P. Muhly, J. Reanult and D. Williams, Equivalence and isomorphism for groupoid C*-algebras,, J. Operator Theory, 17 (1987), 3.

[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, 116 (1979).

[10]

S. Zakrzewski, Quantum and classical pseudogroups I,, Comm. Math. Phys., 134 (1990), 347. doi: doi:10.1007/BF02097706.

show all references

References:
[1]

C. Anantharaman-Delaroche and J. Renault, "Amenable groupoids,", Monographie de L'Enseignement Mathematique No 36, 36 (2000).

[2]

M. Buneci, Groupoid C*-algebras,, Surveys in Mathematics and its Applications, 1 (2006), 71.

[3]

M. Buneci, A category of singly generated dynamical systems,, in, (2007), 122.

[4]

M. Buneci, Groupoid categories,, in, 8 (2008), 27.

[5]

M. Buneci and P. Stachura, Morphisms of locally compact groupoids endowed with Haar systems,, , ().

[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.

[7]

P. Muhly, J. Reanult and D. Williams, Equivalence and isomorphism for groupoid C*-algebras,, J. Operator Theory, 17 (1987), 3.

[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, 116 (1979).

[10]

S. Zakrzewski, Quantum and classical pseudogroups I,, Comm. Math. Phys., 134 (1990), 347. doi: doi:10.1007/BF02097706.

[1]

Howard A. Levine, Yeon-Jung Seo, Marit Nilsen-Hamilton. A discrete dynamical system arising in molecular biology. Discrete & Continuous Dynamical Systems - B, 2012, 17 (6) : 2091-2151. doi: 10.3934/dcdsb.2012.17.2091

[2]

Navin Keswani. Homotopy invariance of relative eta-invariants and $C^*$-algebra $K$-theory. Electronic Research Announcements, 1998, 4: 18-26.

[3]

Søren Eilers. C *-algebras associated to dynamical systems. Discrete & Continuous Dynamical Systems - A, 2006, 15 (1) : 177-192. doi: 10.3934/dcds.2006.15.177

[4]

David Cheban. Belitskii--Lyubich conjecture for $C$-analytic dynamical systems. Discrete & Continuous Dynamical Systems - B, 2015, 20 (3) : 945-959. doi: 10.3934/dcdsb.2015.20.945

[5]

P.K. Newton. The dipole dynamical system. Conference Publications, 2005, 2005 (Special) : 692-699. doi: 10.3934/proc.2005.2005.692

[6]

Aleksandar Zatezalo, Dušan M. Stipanović. Control of dynamical systems with discrete and uncertain observations. Discrete & Continuous Dynamical Systems - A, 2015, 35 (9) : 4665-4681. doi: 10.3934/dcds.2015.35.4665

[7]

Karl P. Hadeler. Quiescent phases and stability in discrete time dynamical systems. Discrete & Continuous Dynamical Systems - B, 2015, 20 (1) : 129-152. doi: 10.3934/dcdsb.2015.20.129

[8]

B. Coll, A. Gasull, R. Prohens. On a criterium of global attraction for discrete dynamical systems. Communications on Pure & Applied Analysis, 2006, 5 (3) : 537-550. doi: 10.3934/cpaa.2006.5.537

[9]

Jean-Luc Chabert, Ai-Hua Fan, Youssef Fares. Minimal dynamical systems on a discrete valuation domain. Discrete & Continuous Dynamical Systems - A, 2009, 25 (3) : 777-795. doi: 10.3934/dcds.2009.25.777

[10]

Paul L. Salceanu, H. L. Smith. Lyapunov exponents and persistence in discrete dynamical systems. Discrete & Continuous Dynamical Systems - B, 2009, 12 (1) : 187-203. doi: 10.3934/dcdsb.2009.12.187

[11]

Mostafa Abounouh, H. Al Moatassime, J. P. Chehab, S. Dumont, Olivier Goubet. Discrete Schrödinger equations and dissipative dynamical systems. Communications on Pure & Applied Analysis, 2008, 7 (2) : 211-227. doi: 10.3934/cpaa.2008.7.211

[12]

Adina Luminiţa Sasu, Bogdan Sasu. Discrete admissibility and exponential trichotomy of dynamical systems. Discrete & Continuous Dynamical Systems - A, 2014, 34 (7) : 2929-2962. doi: 10.3934/dcds.2014.34.2929

[13]

Piotr Oprocha. Chain recurrence in multidimensional time discrete dynamical systems. Discrete & Continuous Dynamical Systems - A, 2008, 20 (4) : 1039-1056. doi: 10.3934/dcds.2008.20.1039

[14]

Jacobo Pejsachowicz, Robert Skiba. Topology and homoclinic trajectories of discrete dynamical systems. Discrete & Continuous Dynamical Systems - S, 2013, 6 (4) : 1077-1094. doi: 10.3934/dcdss.2013.6.1077

[15]

Robert Skiba, Nils Waterstraat. The index bundle and multiparameter bifurcation for discrete dynamical systems. Discrete & Continuous Dynamical Systems - A, 2017, 37 (11) : 5603-5629. doi: 10.3934/dcds.2017243

[16]

Dorota Bors, Robert Stańczy. Dynamical system modeling fermionic limit. Discrete & Continuous Dynamical Systems - B, 2018, 23 (1) : 45-55. doi: 10.3934/dcdsb.2018004

[17]

Xiangnan He, Wenlian Lu, Tianping Chen. On transverse stability of random dynamical system. Discrete & Continuous Dynamical Systems - A, 2013, 33 (2) : 701-721. doi: 10.3934/dcds.2013.33.701

[18]

Jianfeng Feng, Mariya Shcherbina, Brunello Tirozzi. Dynamical behaviour of a large complex system. Communications on Pure & Applied Analysis, 2008, 7 (2) : 249-265. doi: 10.3934/cpaa.2008.7.249

[19]

Artem Dudko, Rostislav Grigorchuk. On spectra of Koopman, groupoid and quasi-regular representations. Journal of Modern Dynamics, 2017, 11: 99-123. doi: 10.3934/jmd.2017005

[20]

Richard H. Cushman, Jędrzej Śniatycki. On Lie algebra actions. Discrete & Continuous Dynamical Systems - S, 2018, 0 (0) : 1-15. doi: 10.3934/dcdss.2020066

2017 Impact Factor: 1.179

Metrics

  • PDF downloads (8)
  • HTML views (0)
  • Cited by (1)

Other articles
by authors

[Back to Top]