Topological transitivity of the normalized maps induced by linear operators. (English) Zbl 1515.47008
Summary: 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.
MSC:
| 47A16 | Cyclic vectors, hypercyclic and chaotic operators |
| 37B05 | Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) |
Keywords:
topological transitivity; supercyclicity; projective transformation; linear transformation; cone transitivityReferences:
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