English

Hamiltonian systems and monotone twist mappings for braids

Dynamical Systems 2025-11-26 v1

Abstract

In 1986, Moser showed that for a given area-preserving map, there exists a Hamiltonian system that realizes it on the Poincar\'e section. Using his technique, we show that for any braid, there exists a Hamiltonian system whose orbits realize the given braid. In particular, when the braid is pseudo-Anosov, so is the Poincar\'e map of the corresponding Hamiltonian.

Keywords

Cite

@article{arxiv.2511.19927,
  title  = {Hamiltonian systems and monotone twist mappings for braids},
  author = {Yuika Kajihara and Mitsuru Shibayama},
  journal= {arXiv preprint arXiv:2511.19927},
  year   = {2025}
}