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ArticleOriginal scientific text

Title

Quantum geometry of noncommutative Bernoulli shifts

Authors 1

Affiliations

  1. Institute of Theoretical Physics and Astrophysics, University of Gdańsk, Wita Stwosza 57, 80-952 Gdańsk, Poland

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.

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Banach Center Publications
1998/43/1
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Pages:
25-29
Main language of publication
English
Published
1998
Exact and natural sciences