We investigate the existence of a common hypercyclic vector for family $(T_\lambda)_{\lambda\in \Lambda}$ hypercyclic operators acting on same Banach space $X$. give positive and negative results involving dimension $\Lambda$ regularity each map $\lambda\in \Lambda\mapsto T_\lambda^n x$, $x\in X$, $n\in\mathbb N$.

The question of whether a hypercyclic operator T acting on Fréchet algebra X admits or not an vectors (but 0) has been addressed in the recent literature. In this paper we give new criteria and characterisations context convolution operators H(C) backward shifts general sequence algebra. Analogous questions arise for stronger properties like frequent hypercyclicity. trend sufficient condition w...

In this paper we characterize hypercyclic sequences of weighted translation operators on an Orlicz space in the context locally compact hypergroups.

In this paper we introduce and study the notion of hypercyclicity for iterated function systems (IFS) operators. We prove that a linear IFS, implies sensitivity if an IFS is abelian, then also multi-sensitivity hence thick sensitivity. give some equivalent conditions as well weakly mixing