Strong closing lemmas in Hamiltonian dynamics
Symplectic Geometry
2025-12-08 v1 Differential Geometry
Dynamical Systems
Abstract
This survey focuses on strong closing lemmas in Hamiltonian dynamics that are proved using spectral invariants (also known as action selectors) in symplectic geometry. We review strong closing lemmas in low-dimensional Hamiltonian dynamics (Reeb flows on contact three-manifolds and area-preserving maps on symplectic surfaces) and outline the key ideas behind their proofs. We also discuss results concerning strong closing lemmas in high-dimensional Hamiltonian dynamics, as well as analogous results for minimal hypersurfaces.
Cite
@article{arxiv.2512.05523,
title = {Strong closing lemmas in Hamiltonian dynamics},
author = {Kei Irie},
journal= {arXiv preprint arXiv:2512.05523},
year = {2025}
}
Comments
19 pages. Revised a version submitted to the Proceedings of the ICM 2026