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.
Full text available as:
 | PDF - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader 415 Kb |
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 |
Download Statistics: last 4 weeks
Repository Staff Only: edit this item