3 papers
math.SG2025
Integrable systems with symmetries: toric, semitoric, and beyond
Joseph Palmer
This article presents an overview of the theory of integrable systems with symmetries, focusing on toric systems, semitoric systems, and their classifications via decorated polygon…
math.SG2023
The twisting index in semitoric systems
Jaume Alonso, Sonja Hohloch, Joseph Palmer
Semitoric integrable systems were symplectically classified by Pelayo and Vu Ngoc in 2009-2011 in terms of five invariants. Four of these invariants were already well-understood pr…
math.SG2019
Semitoric systems of non-simple type
Joseph Palmer, Álvaro Pelayo, Xiudi Tang
Within integrable systems, the class of so called "semitoric" integrable systems in dimension four has attracted a lot of attention in recent years, especially since fundamental ex…