A review of some recent work on hypercyclicity

作者：Dodson Christopher Terence John^*

来源：Balkan Journal of Geometry and Its Applications, 2014, 19(1): 22-41.

• Banach space
• Hilbert space
• Frechet space
• bundles
• hypercyclicity
• operator

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.

• 出版日期2014