Hypersemitoric systems are 2-degree-of-freedom integrable systems on 4-dimensional
symplectic manifolds that have an underlying 𝕊 1-symmetry and no degenerate singularities …

We discuss normal forms and symplectic invariants of parabolic orbits and cuspidal tori in
integrable Hamiltonian systems with two degrees of freedom. Such singularities appear in …

In this article, we introduce b-semitoric systems as a generalization of semitoric systems,
specifically tailored for b-symplectic manifolds. The objective of this article is to furnish a …

Semitoric systems are a type of four-dimensional integrable system for which one of the
integrals generates a global S1-action; these systems were classified by Pelayo and Vu …

The goal of the paper is to develop a systematic approach to the study of (possibly
degenerate) singularities of integrable systems and their structural stability. Following …

The aim of this paper is to give new insights about families of integrable systems lifting a
Hamiltonian $ S^ 1$-space. Specifically, we study one-parameter families $(M^ 4,\omega …

We show that all compact four-dimensional Hamiltonian S1-spaces can be extended to a
completely integrable system on the same manifold such that all singularities are non …

This survey gives a short and comprehensive introduction to a class of finite-dimensional
integrable systems known as hypersemitoric systems, recently introduced by Hohloch and …

In this paper, we study singularities of the Lagrangian fibration given by a completely
integrable system. We prove that a nondegenerate singular fiber satisfying the so-called …

We show that every parabolic orbit of a two-degree-of-freedom integrable system admits a
C^ ∞-smooth Hamiltonian circle action, which is persistent under small integrable C^ ∞ …