Symplectic topology of integrable hamiltonian systems, I : Arnold-Liouville with singularities
Nguyen Tien Zung (1996)
Compositio Mathematica
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Nguyen Tien Zung (1996)
Compositio Mathematica
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Eva Miranda (2014)
Open Mathematics
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The main purpose of this paper is to present in a unified approach to different results concerning group actions and integrable systems in symplectic, Poisson and contact manifolds. Rigidity problems for integrable systems in these manifolds will be explored from this perspective.
K, Fazeela, Subramanian Moosath, K.S. (2007)
Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică
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David T. Gay, Margaret Symington (2009)
Journal of the European Mathematical Society
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A near-symplectic structure on a 4-manifold is a closed 2-form that is symplectic away from the 1-dimensional submanifold along which it vanishes and that satisfies a certain transversality condition along this vanishing locus. We investigate near-symplectic 4-manifolds equipped with singular Lagrangian torus fibrations which are locally induced by effective Hamiltonian torus actions. We show how such a structure is completely characterized by a singular integral affine structure on...
Christopher Allday (1998)
Banach Center Publications
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Akio Hattori (1998)
Banach Center Publications
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The aim of this article is to answer a question posed by J. Oprea in his talk at the Workshop "Homotopy and Geometry".
Ely Kerman, François Lalonde (2003)
Annales de l’institut Fourier
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In this note we consider the length minimizing properties of Hamiltonian paths generated by quasi-autonomous Hamiltonians on symplectically aspherical manifolds. Motivated by the work of Polterovich and Schwarz, we study the role, in the Floer complex of the generating Hamiltonian, of the global extrema which remain fixed as the time varies. Our main result determines a natural condition which implies that the corresponding path minimizes the positive Hofer length. We use this to prove...
Alfred Künzle (1996)
Banach Center Publications
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The purpose of this paper is to develop the basics of a theory of Hamiltonian systems with non-differentiable Hamilton functions which have become important in symplectic topology. A characteristic differential inclusion is introduced and its equivalence to Hamiltonian inclusions for certain convex Hamiltonians is established. We give two counterexamples showing that basic properties of smooth systems are violated for non-smooth quasiconvex submersions, e.g. even the energy conservation...