Common hypercyclic vectors for high dimensional families of operators

Abstract

Let $(T\_\lambda )\_\lambda \in \Lambda$ be a family of operators acting on a $F$-space $X$, where the parameter space $\Lambda$ is a subset of ${\mathbb{R}}^d$. We give sufficient conditions on the family to yield the existence of a vector $x\in X$ such that, for any $\lambda \in \Lambda$, the set $\{T\_{\lambda }^{n}x;n\ge 1\}$ is dense in $X$. We obtain results valid for any value of $d\ge 1$ whereas the previously known results where restricted to $d=1$. Our methods also shed new light on the one-dimensional case.

References in corpus (2)

• Existence of common hypercyclic vectors for translation operators
• Common hypercyclic functions for translation operators with large gaps II