A non-autonomous Hamiltonian diffeomorphism with roots of all orders

Nicolas Grunder; Baptiste Serraille

A non-autonomous Hamiltonian diffeomorphism with roots of all orders

Symplectic Geometry 2025-10-27 v2 Dynamical Systems

Authors: Nicolas Grunder , Baptiste Serraille

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 $\mathbb Q$ .

Keywords

Hamiltonian diffeomorphism roots of all orders Anosov-Katok construction non-autonomous dynamics

Cite

@article{arxiv.2502.06467,
  title  = {A non-autonomous Hamiltonian diffeomorphism with roots of all orders},
  author = {Nicolas Grunder and Baptiste Serraille},
  journal= {arXiv preprint arXiv:2502.06467},
  year   = {2025}
}

Comments

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

A non-autonomous Hamiltonian diffeomorphism with roots of all orders

Abstract

Keywords

Cite

Comments

Related papers