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, ...

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 ...

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 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 ...

Hypercycles are information integration systems which are thought to overcome the information crisis of prebiotic evolution by ensuring the coexistence of several short templates. For imperfect template replication, we ...

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 ...