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2012.38: A review of some recent work on hypercyclicity

2012.38: CTJ Dodson (2012) A review of some recent work on hypercyclicity. In: Workshop celebrating the 65 birthday of L. A. Cordero, 27-29 June 2012, Santiago de Compostela, Spain.

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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. This article gives a brief review of some recent work on hypercyclicity of operators on Banach, Hilbert and Frechet spaces.

Item Type:Conference or Workshop Item (Lecture)
Uncontrolled Keywords:Banach space, Hilbert space, Frechet space, bundles, hypercyclicity
Subjects:MSC 2000 > 16 Associative rings and algebras
MSC 2000 > 37 Dynamical systems and ergodic theory
MSC 2000 > 47 Operator theory
MSC 2000 > 58 Global analysis, analysis on manifolds
MIMS number:2012.38
Deposited By:Prof CTJ Dodson
Deposited On:23 April 2012

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