منابع مشابه
Weak mixing and eigenvalues for Arnoux-Rauzy sequences
— We define by simple conditions two wide subclasses of the socalled Arnoux-Rauzy systems; the elements of the first one share the property of (measure-theoretic) weak mixing, thus we generalize and improve a counterexample to the conjecture that these systems are codings of rotations; those of the second one have eigenvalues, which was known hitherto only for a very small set of examples. Résu...
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We consider the occurrence of unimodular eigenvalues for palindromic eigenvalue problems associated with the matrix polynomial Pn(λ) ≡ ∑n i=0Aiλ i where Ai = An−i with M∗ ≡ M , M or PMP (P 2 = I). From the properties of palindromic eigenvalues and their characteristic polynomials, we show that eigenvalues are not generically excluded from the unit circle, thus occurring quite often, except for ...
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A minimal dynamical system (X,T ) is called quasi-Bohr if it is a nontrivial equicontinuous extension of a proximal system. We show that if (X,T ) is a minimal dynamical system which is not weakly mixing then some minimal proximal extension of (X, T ) admits a nontrivial quasi-Bohr factor. (In terms of Ellis groups the corresponding statement is: AG′ = G implies weak mixing.) The converse does ...
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 1980
ISSN: 0022-1236
DOI: 10.1016/0022-1236(80)90079-8