Dinâmica no contexto de espaços uniformes e dinâmica dos operadores de convolução sobre H(C^N)

Abstract

In this work we will study several properties of the linear dynamics of convolution operators on the space H(C^N) of all entire functions of infinitely many complex variables, as hypercyclicity, mixing, cyclicity, n-supercyclicity, Li-Yorke chaos and distributional chaos. For the study of the last two, we adapt the well-known concepts on Fréchet spaces to the context of uniform spaces. We will present the results that convolution operators on H(C^N) are not cycllic or n-supercyclic (in particular they are not hypercyclic), but the convolution operators that are not scalar multiple of the identity are mixing and Li-Yorke chaotic. Besides, we will prove a original result that theses operators are distributionally chaotic.