2 00 3 a Geometric Approach to Voiculescu - Brown Entropy
نویسنده
چکیده
A basic problem in dynamics is to identify systems with positive entropy, i.e., systems which are “chaotic.” While there is a vast collection of results addressing this issue in topological dynamics, the phenomenon of positive entropy remains by and large a mystery within the broader noncommutative domain of C∗-algebraic dynamics. To shed some light on the noncommutative situation we propose a geometric perspective inspired by work of Glasner and Weiss on topological entropy. This is a written version of the author’s talk at the Winter 2002 Meeting of the Canadian Mathematical Society
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M ar 2 00 3 POSITIVE VOICULESCU - BROWN ENTROPY IN NONCOMMUTATIVE TORAL AUTOMORPHISMS
We show that the Voiculescu-Brown entropy of a noncommutative toral automorphism arising from a matrix S ∈ GL(d,Z) is at least half the value of the topological entropy of the corresponding classical toral automorphism. We also obtain some information concerning the positivity of local Voiculescu-Brown entropy with respect to single unitaries. In particular we show that if S has no roots of uni...
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