Abstract
The research of dynamics of linear operators mainly involves hypercyclic, chaotic, mixing properties and so on. It has close links with complex analysis, theory of operator and differential geometry, with a wide range of applications. Some linear operators on infinite dimensional spaces can display interesting dynamical properties. In particular, hypercyclicity is an essentially infinite dimensional property, when iterations of the operator generate a dense subspace. A local convex complete metric space admits a hypercyclic operator if and only if it is separable and infinite dimensional. Over more than two decades, the study of dynamics of linear operators has turned into a very active research area and many fascinating research results have been given. In this paper, we will systematically summarize the contents of dynamics of linear operators and will give a brief review of the recent research results about wonderful dynamical properties of linear operators, among which related conclusions of our research group are involved.
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