Séminaire et groupe de travail d’Algèbre du 23 janvier
This talk concerns the behavior of iterates of linear transformations (in an infinite dimensional setting). Particularly, the phenomenon of hypercyclicity, where there exists a vector with dense orbit under a linear operator. By replacing the orbit of a single vector with the orbits of an uncountable set of vectors, we obtain the weaker notion of supercyclicity. The connection between the two is investigated in an article of S. Charpentier, R. Ernst, Q. Menet. In this talk we plan to highlight how the underlying group structure of a specific set can offer a better comprehension of these orbits. Getting a further insight into this group structure allows us to generalize the problems studied in the aforementioned article.