Hypercyclic bilinear operators on Banach spaces

Abstract

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 hypercyclic operators on arbitrary infinite dimensional separable Banach spaces. We also prove an existence result about symmetric bihypercyclic bilinear operators, answering a question by Grosse-Erdman and Kim.