# Quantum geometry of noncommutative Bernoulli shifts

Banach Center Publications (1998)

- Volume: 43, Issue: 1, page 25-29
- ISSN: 0137-6934

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topAlicki, Robert. "Quantum geometry of noncommutative Bernoulli shifts." Banach Center Publications 43.1 (1998): 25-29. <http://eudml.org/doc/208847>.

@article{Alicki1998,

abstract = {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.},

author = {Alicki, Robert},

journal = {Banach Center Publications},

keywords = {noncommutative dynamical system; two-dimensional noncommutative differential manifold; positive Lyapunov exponents; quantum Bernoulli shift; noncommutative Pesin theorem},

language = {eng},

number = {1},

pages = {25-29},

title = {Quantum geometry of noncommutative Bernoulli shifts},

url = {http://eudml.org/doc/208847},

volume = {43},

year = {1998},

}

TY - JOUR

AU - Alicki, Robert

TI - Quantum geometry of noncommutative Bernoulli shifts

JO - Banach Center Publications

PY - 1998

VL - 43

IS - 1

SP - 25

EP - 29

AB - 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.

LA - eng

KW - noncommutative dynamical system; two-dimensional noncommutative differential manifold; positive Lyapunov exponents; quantum Bernoulli shift; noncommutative Pesin theorem

UR - http://eudml.org/doc/208847

ER -

## References

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