Quantum geometry of noncommutative Bernoulli shifts

Volume 43 / 1998

Robert Alicki Banach Center Publications 43 (1998), 25-29 DOI: 10.4064/-43-1-25-29


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.


  • Robert Alicki

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