A counterexample to Lagrangian Poincar\'e recurrence in dimension four
Symplectic Geometry
2026-01-14 v4 Dynamical Systems
Abstract
Counterexamples to Lagrangian Poincar\'e recurrence were recently found in dimensions greater than six by Bro\'ci\'c and Shelukhin. We construct counterexamples in dimension four using almost toric fibrations.
Cite
@article{arxiv.2410.24102,
title = {A counterexample to Lagrangian Poincar\'e recurrence in dimension four},
author = {Joel Schmitz},
journal= {arXiv preprint arXiv:2410.24102},
year = {2026}
}
Comments
7 pages, 3 figures; v2: added Remark 3.5; v3: refined Remark 3.5; v4: some clarifications, added Remark 2.1