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Fiber connectivity and bifurcation diagrams of almost toric integrable systems

Abstract : We describe the bifurcation diagrams of almost toric integrable Hamiltonian systems on a four dimensional symplectic manifold MM, not necessarily compact. We prove that, under a weak assumption, the connectivity of the fibers of the induced singular Lagrangian fibration M→R^2 can be detected from the bifurcation diagram alone. In this case, it is possible to give a detailed description of the image of the fibration.
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Álvaro Pelayo, Tudor S. Ratiu, San Vũ Ngoc. Fiber connectivity and bifurcation diagrams of almost toric integrable systems. Journal of Symplectic Geometry, International Press, 2015, 13 (2), pp.343-386. ⟨10.4310/JSG.2015.v13.n2.a4⟩. ⟨hal-01398293⟩

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