A Geometric Approach to Voiculescu-Brown Entropy

[摘要] A basic problem in dynamics is to identify systems with positive entropy, i.e., systems which are ``chaotic.'' Whilethere 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 talkat the Winter 2002 Meeting of the Canadian Mathematical Societyin Ottawa, Ontario.

[学科分类] 数学（综合）

[关键词] Hardy operator;Hardy-Steklov operator;compactness;boundedness;star-shaped regions