Dynamics of shift operators
Bingzhe Hou, Gongfu Liao, Yang Cao · 2012
Abstract. In this article, some dynamical properties of unilateral backward weighed shift operators are considered. We obtain the complete classification for shift operators with constant weight in the sense of topologically conju-gacy. Sensitivity and Li-Yorke chaos are also considered. We prove that they are equivalent for unilateral backward weighted shift operators. At the end, we show an interesting phenomenon: The closure of every bounded or-bit under a Devaney chaotic weighted shift operator is compact. However, there exists a bounded orbit with empty omega-limit set under a sensitive weighted shift operator. 1. Introduction and