# American Institute of Mathematical Sciences

February  2006, 15(1): 177-192. doi: 10.3934/dcds.2006.15.177

## C *-algebras associated to dynamical systems

 1 Department of Mathematics, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen Ø, Denmark

Received  December 2004 Revised  August 2005 Published  February 2006

We give an overview of important areas of contact between dynamical systems and operator algebras in the context of classification, describing two different invariant ways of associating a C *-algebra to certain dynamical systems and comparing them in the case of substitutional shift spaces.
Citation: Søren Eilers. C *-algebras associated to dynamical systems. Discrete & Continuous Dynamical Systems, 2006, 15 (1) : 177-192. doi: 10.3934/dcds.2006.15.177
 [1] Nigel Higson and Gennadi Kasparov. Operator K-theory for groups which act properly and isometrically on Hilbert space. Electronic Research Announcements, 1997, 3: 131-142. [2] Steven T. Piantadosi. Symbolic dynamics on free groups. Discrete & Continuous Dynamical Systems, 2008, 20 (3) : 725-738. doi: 10.3934/dcds.2008.20.725 [3] Jim Wiseman. Symbolic dynamics from signed matrices. Discrete & Continuous Dynamical Systems, 2004, 11 (2&3) : 621-638. doi: 10.3934/dcds.2004.11.621 [4] George Osipenko, Stephen Campbell. Applied symbolic dynamics: attractors and filtrations. Discrete & Continuous Dynamical Systems, 1999, 5 (1) : 43-60. doi: 10.3934/dcds.1999.5.43 [5] Michael Hochman. A note on universality in multidimensional symbolic dynamics. Discrete & Continuous Dynamical Systems - S, 2009, 2 (2) : 301-314. doi: 10.3934/dcdss.2009.2.301 [6] Jose S. Cánovas, Tönu Puu, Manuel Ruiz Marín. Detecting chaos in a duopoly model via symbolic dynamics. Discrete & Continuous Dynamical Systems - B, 2010, 13 (2) : 269-278. doi: 10.3934/dcdsb.2010.13.269 [7] Nicola Soave, Susanna Terracini. Symbolic dynamics for the $N$-centre problem at negative energies. Discrete & Continuous Dynamical Systems, 2012, 32 (9) : 3245-3301. doi: 10.3934/dcds.2012.32.3245 [8] Dieter Mayer, Fredrik Strömberg. Symbolic dynamics for the geodesic flow on Hecke surfaces. Journal of Modern Dynamics, 2008, 2 (4) : 581-627. doi: 10.3934/jmd.2008.2.581 [9] Frédéric Naud. Birkhoff cones, symbolic dynamics and spectrum of transfer operators. Discrete & Continuous Dynamical Systems, 2004, 11 (2&3) : 581-598. doi: 10.3934/dcds.2004.11.581 [10] Fryderyk Falniowski, Marcin Kulczycki, Dominik Kwietniak, Jian Li. Two results on entropy, chaos and independence in symbolic dynamics. Discrete & Continuous Dynamical Systems - B, 2015, 20 (10) : 3487-3505. doi: 10.3934/dcdsb.2015.20.3487 [11] David Ralston. Heaviness in symbolic dynamics: Substitution and Sturmian systems. Discrete & Continuous Dynamical Systems - S, 2009, 2 (2) : 287-300. doi: 10.3934/dcdss.2009.2.287 [12] Kengo Matsumoto. Continuous orbit equivalence of topological Markov shifts and KMS states on Cuntz–Krieger algebras. Discrete & Continuous Dynamical Systems, 2020, 40 (10) : 5897-5909. doi: 10.3934/dcds.2020251 [13] Kengo Matsumoto. $C^*$-algebras associated with asymptotic equivalence relations defined by hyperbolic toral automorphisms. Electronic Research Archive, 2021, 29 (4) : 2645-2656. doi: 10.3934/era.2021006 [14] Mike Boyle. The work of Mike Hochman on multidimensional symbolic dynamics and Borel dynamics. Journal of Modern Dynamics, 2019, 15: 427-435. doi: 10.3934/jmd.2019026 [15] Rostislav Grigorchuk, Volodymyr Nekrashevych. Self-similar groups, operator algebras and Schur complement. Journal of Modern Dynamics, 2007, 1 (3) : 323-370. doi: 10.3934/jmd.2007.1.323 [16] Adam Kanigowski, Federico Rodriguez Hertz, Kurt Vinhage. On the non-equivalence of the Bernoulli and $K$ properties in dimension four. Journal of Modern Dynamics, 2018, 13: 221-250. doi: 10.3934/jmd.2018019 [17] Anke D. Pohl. Symbolic dynamics for the geodesic flow on two-dimensional hyperbolic good orbifolds. Discrete & Continuous Dynamical Systems, 2014, 34 (5) : 2173-2241. doi: 10.3934/dcds.2014.34.2173 [18] Nicola Soave, Susanna Terracini. Addendum to: Symbolic dynamics for the $N$-centre problem at negative energies. Discrete & Continuous Dynamical Systems, 2013, 33 (8) : 3825-3829. doi: 10.3934/dcds.2013.33.3825 [19] Lorenzo Sella, Pieter Collins. Computation of symbolic dynamics for two-dimensional piecewise-affine maps. Discrete & Continuous Dynamical Systems - B, 2011, 15 (3) : 739-767. doi: 10.3934/dcdsb.2011.15.739 [20] Snir Ben Ovadia. Symbolic dynamics for non-uniformly hyperbolic diffeomorphisms of compact smooth manifolds. Journal of Modern Dynamics, 2018, 13: 43-113. doi: 10.3934/jmd.2018013

2020 Impact Factor: 1.392