It is known that homogeneous polynomials on Banach spaces cannot be hypercyclic, but there are examples of hypercyclic homogeneous polynomials on some non-normable Fréchet spaces. We show the existence of hypercyclic ...

We study hypercyclicity properties of a family of non-convolution operators defined on the spaces of entire functions on CN. These operators are a composition of a differentiation operator and an affine composition operator, ...

We study the dynamics induced by an m-linear operator. We answer a question of Bès and Conejero showing an example of an m-linear hypercyclic operator acting on a Banach space. Moreover, we prove the existence of m-linear ...

A result of Godefroy and Shapiro states that the convolution operators on the space of entire functions on Cn, which are not multiples of identity, are hypercyclic. Analogues of this result have appeared for some spaces ...

A theorem of Godefroy and Shapiro states that non-trivial convolution operators on the space of entire functions on (Formula Presented.) are hypercyclic. Moreover, it was shown by Bonilla and Grosse-Erdmann that they have ...

In this article we study the hypercyclic behavior of non-convolution operators defined on spaces of analytic functions of different holomorphy types over Banach spaces. The operators in the family we analyze are a composition ...

In the early 1970's Eisenberg and Hedlund investigated relationships between expansivity and spectrum of operators on Banach spaces. In this paper we establish relationships between notions of expansivity and hypercyclicity, ...

We study the dynamics induced by homogeneous polynomials on Banach spaces. It is known that no homogeneous polynomial defined on a Banach space can have a dense orbit. We show a simple and natural example of a homogeneous ...

En este artículo divulgativo se presentan los conceptos básicos sobre hiperciclidad, ejemplos clásicos de operadores hipercíclicos en espacios de Fréchet y propiedades importantes de operadores hipercíclicos en espacios ...