Symplectic topology and hamiltonian dynamics
I. Ekeland, H. Hofer (1987-1988)
Séminaire Équations aux dérivées partielles (Polytechnique)
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I. Ekeland, H. Hofer (1987-1988)
Séminaire Équations aux dérivées partielles (Polytechnique)
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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...
Takeo Nishinou (2004)
Mathematica Bohemica
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We perform symplectic embeddings of ‘thin’ discs into a small ball in arbitrary dimension, using the symplectic folding construction.
Claude Viterbo (1991)
Journées équations aux dérivées partielles
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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...
L. Polterovich (1996)
Geometric and functional analysis
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H. Hofer, I. Ekeland (1988/89)
Mathematische Zeitschrift
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Karl Friedrich Siburg (1993)
Manuscripta mathematica
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Helmut Hofer, Ivar Ekeland (1990)
Mathematische Zeitschrift
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Stefano Vidussi (2007)
Journal of the European Mathematical Society
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We show that there exists a family of simply connected, symplectic 4-manifolds such that the (Poincaré dual of the) canonical class admits both connected and disconnected symplectic representatives. This answers a question raised by Fintushel and Stern.