Mixing properties of one-dimensional
Proc. Amer. Math. Soc. 125 (1997), 1755-1766
Primary 47A35, 22D25; Secondary 28D05, 46L05
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Abstract: We study a class of endomorphisms on the space of bi-infinite sequences over a finite set, and show that such a map is onto if and only if it is measure-preserving. A class of dynamical systems arising from these endomorphisms are strongly mixing, and some of them even -mixing. Some of these are isomorphic to the one-sided shift on in both the topological and measure-theoretical sense. Such dynamical systems can be associated to , the Cuntz-algebra of order , in a natural way.
Ola Bratteli, Palle E.T. Jørgensen and Geoffrey L. Price. Endomorphisms of . Proc. Symp. Pure Math. Am. math. soc. 1995. (ed. I.E. Segal.) To appear.
Cuntz, Simple 𝐶*-algebras generated by isometries,
Comm. Math. Phys. 57 (1977), no. 2, 173–185. MR 0467330
A. Hedlund, Endomorphisms and automorphisms of the shift dynamical
system, Math. Systems Theory 3 (1969), 320–375.
0259881 (41 #4510)
Matsumoto, 𝐶*-algebras associated with cellular
automata, Math. Scand. 75 (1994), no. 2,
195–216. MR 1319731
Shirvani and T.
D. Rogers, On ergodic one-dimensional cellular automata, Comm.
Math. Phys. 136 (1991), no. 3, 599–605. MR 1099698
Walters, An introduction to ergodic theory, Graduate Texts in
Mathematics, vol. 79, Springer-Verlag, New York, 1982. MR 648108
- Ola Bratteli, Palle E.T. Jørgensen and Geoffrey L. Price. Endomorphisms of . Proc. Symp. Pure Math. Am. math. soc. 1995. (ed. I.E. Segal.) To appear.
- Joachim Cuntz, Simple -algebras generated by isometries. Commun. Math. Phys. 57, 173-185 (1977). MR 57:7189
- G.A. Hedlund. Endomorphisms and automorphisms of the shift dynamical system. Math. Syst. theory 3, 320-375 (1970). MR 41:4510
- Kengo Matsumoto. -algebras associated width dynamical systems. Math. Scand. 75, 195-216 (1994). MR 96a:46120
- M. Shirvani and T.D. Rogers. On ergodic one-Dimensional Cellular Automata, Commun. Math. Phys. 136, 599-605 (1991). MR 92j:58057
- Peter Walters. An introduction to ergodic theory. Springer (1982). MR 84e:28017
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Department of Mathematics, University of Oslo, Box 1053, 0316 Oslo, Norway
Received by editor(s):
October 23, 1995
Received by editor(s) in revised form:
December 13, 1995
Palle E. Jørgensen
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