A non-autonomous Hamiltonian diffeomorphism with roots of all orders

TL;DR

This paper constructs non-autonomous Hamiltonian diffeomorphisms with roots of all orders using an adapted Anosov-Katok method, answering a question by Mann and Shelukin, and also builds a rational action on manifolds with specific continuity properties.

Contribution

It introduces a novel construction of Hamiltonian diffeomorphisms with roots of all orders and explores rational actions with unique topological features.

Findings

Constructed non-autonomous Hamiltonian diffeomorphisms with roots of all orders.

Provided an example of a rational action on manifolds with non-$C^0$-continuity.

Answered an open question by Mann and Shelukin.

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 $\mathbb Q$.