Semitoric integrable systems on symplectic 4-manifolds
By 'Alvaro Pelayo, San Vũ Ngọc. 2008
102 citations recorded by the source corpus.
Let (M,ω) be a symplectic 4-manifold. A semitoric integrable system on (M,ω) is a pair of smooth functions J,H∈C ∞(M,ℝ) for which J generates a Hamiltonian S1-action and the Poisson brackets {J,H} vanish. We shall introduce new global symplectic invariants for these systems; some of these invariants encode topological or geometric aspects, while others encode analytical information about the singularities and how they stand with respect to the system. Our goal is to prove that a semitoric system is completely determined by the invariants we introduce.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/9590249c7729bf6b2a615abcbfbae344e84d22d2
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Symplectic theory of completely integrable Hamiltonian systems (2011, unknown): “The map f satisfies further properties [87], which are relevant for the uniqueness proof.”
- Fixed points of symplectic periodic flows (2010, background): “diagrams in the modern global theory of integrable systems, see [17], [ 13 ], [14].”
- Constructing integrable systems of semitoric type (2009, methodology): “We recall the definition of the invariants that we assigned toa semitoric integrable system in our previous paper [17], to which we refer to further details.”