A review of some recent work on hypercyclicity
Abstract
Even linear operators on infinite-dimensional spaces can display interesting dynamical properties and yield important links among functional analysis, differential and global geometry and dynamical systems, with a wide range of applications. In particular, hypercyclicity is an essentially infinite-dimensional property, when iterations of the operator generate a dense subspace. A Frechet space admits a hypercyclic operator if and only if it is separable and infinite-dimensional. However, by considering the semigroups generated by multiples of operators, it is possible to obtain hypercyclic behaviour on finite dimensional spaces. This article gives a brief review of some recent work on hypercyclicity of operators on Banach, Hilbert and Frechet spaces.
Keywords
Cite
@article{arxiv.1211.4390,
title = {A review of some recent work on hypercyclicity},
author = {C. T. J. Dodson},
journal= {arXiv preprint arXiv:1211.4390},
year = {2012}
}
Comments
Invited paper, Workshop celebrating the 65 birthday of L. A. Cordero, Santiago de Compostela, June 27-29, 2012. 15 pages 116 references