We construct an example of a noncommutative dynamical system defined over a two dimensional noncommutative differential manifold with two positive Lyapunov exponents equal to ln d each. This dynamical system is isomorphic to the quantum Bernoulli shift on the half-chain with the quantum dynamical entropy equal to 2 ln d. This result can be interpreted as a noncommutative analog of the isomorphism between the classical one-sided Bernoulli shift and the expanding map of the circle and moreover as an example of the noncommutative Pesin theorem.
@article{bwmeta1.element.bwnjournal-article-bcpv43i1p25bwm,
author = {Alicki, Robert},
title = {Quantum geometry of noncommutative Bernoulli shifts},
journal = {Banach Center Publications},
volume = {43},
year = {1998},
pages = {25-29},
zbl = {0984.46045},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv43i1p25bwm}
}
Alicki, Robert. Quantum geometry of noncommutative Bernoulli shifts. Banach Center Publications, Tome 43 (1998) pp. 25-29. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv43i1p25bwm/
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