Displaying similar documents to “Dynamical entropy of a non-commutative version of the phase doubling”

Entropy of eigenfunctions of the Laplacian in dimension 2

Gabriel Rivière (2010)

Journées Équations aux dérivées partielles

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We study asymptotic properties of eigenfunctions of the Laplacian on compact Riemannian surfaces of Anosov type (for instance negatively curved surfaces). More precisely, we give an answer to a question of Anantharaman and Nonnenmacher [] by proving that the Kolmogorov-Sinai entropy of a semiclassical measure μ for the geodesic flow g t is bounded from below by half of the Ruelle upper bound. (This text has been written for the proceedings of the 37 èmes Journées EDP (Port d’Albret-June, 7-11...

Comparing quantum dynamical entropies

P. Tuyls (1998)

Banach Center Publications

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Last years, the search for a good theory of quantum dynamical entropy has been very much intensified. This is not only due to its usefulness in quantum probability but mainly because it is a very promising tool for the theory of quantum chaos. Nowadays, there are several constructions which try to fulfill this need, some of which are more mathematically inspired such as CNT (Connes, Narnhofer, Thirring), and the one proposed by Voiculescu, others are more inspired by physics such as...

Mixing properties of nearly maximal entropy measures for ℤ d shifts of finite type

E. Robinson, Ayşe Şahin (2000)

Colloquium Mathematicae

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We prove that for a certain class of ℤ d shifts of finite type with positive topological entropy there is always an invariant measure, with entropy arbitrarily close to the topological entropy, that has strong metric mixing properties. With the additional assumption that there are dense periodic orbits, one can ensure that this measure is Bernoulli.

Non-commutative entropy computations for continuous fields and cross-products

Emmanuel Germain (2007)

Annales mathématiques Blaise Pascal

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We present here two non-commutative situations where dynamical entropy estimates are possible. The first result is concerned with automorphisms of cross-products by an exact group that commute with the group action and generalizes the result known for amenable groups. The second is about continuous fields of C * -algebras and C ( X ) -automorphisms. Each result relies on explicit factorization via matrices.

Quantum geometry of noncommutative Bernoulli shifts

Robert Alicki (1998)

Banach Center Publications

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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...

Entropy numbers of general diagonal operators.

Thomas Kühn (2005)

Revista Matemática Complutense

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We determine the asymptotic behavior of the entropy numbers of diagonal operators D: l → l, (x) → (sx), 0 < p,q ≤ ∞, under mild regularity and decay conditions on the generating sequence (σ). Our results extend the known estimates for polynomial and logarithmic diagonals (σ). Moreover, we also consider some exotic intermediate examples like (σ)=exp(-√log k).