Let $T$ be a hypercyclic operator on a Fr\'echet space X. Ansari's Theorem says that any hypercyclic vector $x$ for $T$ is also hypercyclic for $T^{\alpha}$, where $\alpha$ is any positive integer. Equivalently, $x$ is hypercyclic for the sequence $(T^{\alpha n})_n$. A natural question that arises is to characterise which sequences $(\lambda_n)_n$ of positive integers have the property that any hypercyclic vector $x$ for $T$ is also hypercyclic for $(T^{\lambda_n})_n$. In this talk, we will solve this problem when $T$ is in a specific class of hypercyclic operators (for example the characterison is true for Birkhoff's, MacLane's or Rolewicz's operators). Using this characterisation, we can give non-trivial examples of such sequences.

Joint work with St\'ephane Charpentier, Romuald Ernst and Myrto Manolaki.