A review of some recent work on hypercyclicity

Dodson, CTJ (2014) A review of some recent work on hypercyclicity. Balkan Journal of Geometry and Its Applications, 19 (1). pp. 22-41. ISSN 1843-2875

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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. The main part of this article gives a brief review of some recent work on hypercyclicity of operators on Banach, Hilbert and Frechet spaces.

Item Type: Article
Uncontrolled Keywords: Banach space, Hilbert space, Frechet space, bundles, hypercyclicity
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 16 Associative rings and algebras
MSC 2010, the AMS's Mathematics Subject Classification > 37 Dynamical systems and ergodic theory
MSC 2010, the AMS's Mathematics Subject Classification > 47 Operator theory
MSC 2010, the AMS's Mathematics Subject Classification > 58 Global analysis, analysis on manifolds
Depositing User: Prof CTJ Dodson
Date Deposited: 09 Jun 2014
Last Modified: 20 Oct 2017 14:13
URI: http://eprints.maths.manchester.ac.uk/id/eprint/2143

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