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 resultsaddressing this issue in topological dynamics, the phenomenon of positiveentropy remains by and large a mystery within the broader noncommutative domainof C*-algebraic dynamics. To shed some light on the noncommutative situation wepropose a geometric perspective inspired by work of Glasner and Weiss ontopological entropy. This is a written version of the author's talk at theWinter 2002 Meeting of the Canadian Mathematical Society in Ottawa, Ontario.
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