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.
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}
}