A Poincar\'e-Birkhoff Theorem for Asymptotically Unitary Hamiltonian Diffeomorphisms
Symplectic Geometry
2026-04-21 v5 Dynamical Systems
Abstract
We prove that an asymptotically linear Hamiltonian diffeomorphism of the standard symplectic vector space, which is non-degenerate and unitary at infinity and approaches its linear map at infinity quickly enough, has infinitely many periodic points, provided that it satisfies a natural twist condition inspired by the classical Poincar\'e-Birkhoff theorem.
Cite
@article{arxiv.2403.01855,
title = {A Poincar\'e-Birkhoff Theorem for Asymptotically Unitary Hamiltonian Diffeomorphisms},
author = {Leonardo Masci},
journal= {arXiv preprint arXiv:2403.01855},
year = {2026}
}
Comments
59 pages. Major revisions