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.
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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
© Copyright 1997
American Mathematical Society