2025/10/19 by Sepe, Daniele, Tolman, Susan
#53D20. Secondary 37J39 #53D35 #Dynamical Systems (math.DS) #FOS: Mathematics #Primary: 37J35 #Symplectic Geometry (math.SG)
paper · doi:10.48550/arxiv.2510.16976
In an earlier paper, we proved the connectedness of the fibers of every 2n-dimensional integrable system satisfying both: the action extends the action of an (n-1)-dimensional torus which has a proper moment map, and every tall singular point is non-degenerate and no such point has a hyperbolic block and connected T-stabilizer. Unfortunately, these criteria are fairly restrictive. Our main goal in this paper is to find a larger class of integrable systems that has connected fibers by weakening the non-degeneracy assumption above. To achieve this, we introduce ``ephemeral" degenerate singular points, examples of which have appeared in the literature in the context of p : -q resonances and special Lagrangian fibrations. Finally, we construct a family of examples that shows that our main theorem meaningfully extends previous results.