منابع مشابه
Symplectic Rigidity for Anosov Hypersurfaces
There is a canonical exact symplectic structure on the unit tangent bundle of a Riemannian manifold M given by pulling-back the symplectic two form ω and Liouville one form λ from the cotangent bundle T ∗M using the Riemannian metric. The pull-back of λ gives a contact form on level-sets of the length function on TM . The geodesic flow of M is given by the Reeb vectorfield of this contact struc...
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1Jerrold E. Marsden and Tudor S. Ratiu, Introduction to Mechanics and Symmetry, second ed., Chapter 2. 2Serge Lang, Differential and Riemannian Manifolds, p. 150, Theorem 8.1; Mircea Puta, Hamiltonian Mechanical Systems and Geometric Quantization, p. 12, Theorem 1.3.1. 3Andreas Kriegl and Peter W. Michor, The Convenient Setting of Global Analysis, p. 522, §48; Peter W. Michor, Some geometric ev...
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A new tool to study reducibility of a weak symplectic form to a constant one is introduced and used to prove a version of the Darboux theorem more general than previous ones. More precisely, at each point of the considered manifold a Banach space is associated to the symplectic form (dual of the phase space with respect to the symplectic form), and it is shown that the Darboux theorem holds if ...
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ژورنال
عنوان ژورنال: Journal of Symplectic Geometry
سال: 2013
ISSN: 1527-5256,1540-2347
DOI: 10.4310/jsg.2013.v11.n2.a1