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Peer-reviewedCC BYJournal of fixed point theory and Its applications

A non-autonomous Hamiltonian diffeomorphism with roots of all orders.

  • Nicolas Grunder1
  • Baptiste Serraille2
  1. 1Institut de Mathématiques, Université de Neuchâtel, Rue Emile-Argand 11, 2000 Neuchätel, Switzerland.
  2. 2Department of Mathematics, ETH-Zürich, Rämistrasse 101, 8092 Zürich, Switzerland.
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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 Shelukhin. Additionally, we construct an action of the rationals by diffeomorphism on any manifold that is not \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}C0\end{document}C0-continuous with respect to the Euclidean topology on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}ℚ\end{document}Q.

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Cite

BibTeXRIS
BibTeX
@article{grunder2026nonautonomous,
  title = {{A non-autonomous Hamiltonian diffeomorphism with roots of all orders.}},
  author = {Nicolas Grunder and Baptiste Serraille},
  journal = {Journal of fixed point theory and Its applications},
  year = {2026},
  month = may,
  doi = {10.1007/s11784-026-01307-6},
  url = {https://europepmc.org/article/MED/42948237},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - A non-autonomous Hamiltonian diffeomorphism with roots of all orders.
AU  - Nicolas Grunder
AU  - Baptiste Serraille
PY  - 2026
DA  - 2026/05/26
JO  - Journal of fixed point theory and Its applications
DO  - 10.1007/s11784-026-01307-6
UR  - https://europepmc.org/article/MED/42948237
AB  - 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 Shelukhin. Additionally, we construct an action of the rationals by diffeomorphism on any manifold that is not \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}C^0\end{document}C0-continuous with respect to the Euclidean topology on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}ℚ\end{document}Q.
SN  - 1661-7738
SN  - 1661-7746
ER  -