A non-autonomous Hamiltonian diffeomorphism with roots of all orders

Abstract

We present a way of constructing non-autonomous Hamiltonian diffeomorphisms with roots of all orders by adapting the Anosov-Katok construction. This answers a question by Kathryn Mann and Egor Shelukin. Additionally, we construct an action of the rationals by diffeomorphism on any manifold that is not $C^0$-continuous with respect to the Euclidean topology on $\mathbb{Q}$.

v2: 15 pages, added a result on the non C0 continuity of the group Q-action, added more reference, comments welcome