Topological transitivity of the normalized maps induced by linear operators

Abstract

In this article, we provide a simple geometric proof of the following fact: The existence of transitive normalized maps induced by linear operators is possible only when the underlying space's real dimension is either 1 or 2 or infinity. A similar result holds for projective transformation as well.

Keywords

• topological transitivity
• supercyclicity
• projective transformation
• linear transformation
• cone transitivity