A review of some recent work on hypercyclicity

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    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 Fr´echet 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 Fr´echet spaces.
    Original languageEnglish
    Pages (from-to)22-41
    JournalBalkan Journal of Geometry and Its Applications
    Issue number1
    Publication statusPublished - 2014


    • Banach space, Hilbert space, Fr´echet space, bundles, operator, hypercyclicity.


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