Cotangent bundle reduction and Poincaré–Birkhoff normal forms
نویسندگان
چکیده
منابع مشابه
Dirac Cotangent Bundle Reduction
The authors’ recent paper in Reports in Mathematical Physics develops Dirac reduction for cotangent bundles of Lie groups, which is called Lie– Dirac reduction. This procedure simultaneously includes Lagrangian, Hamiltonian, and a variational view of reduction. The goal of the present paper is to generalize Lie–Dirac reduction to the case of a general configuration manifold; we refer to this as...
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Cotangent bundle reduction theory is a basic and well developed subject in which one performs symplectic reduction on cotangent bundles. One starts with a (free and proper) action of a Lie group G on a configuration manifold Q, considers its natural cotangent lift to T ∗Q and then one seeks realizations of the corresponding symplectic or Poisson reduced space. We further develop this theory by ...
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Let Q be a smooth manifold acted upon smoothly by a Lie group G, and let N be the space of G-orbits. The G-action lifts to an action on the total space T∗Q of the cotangent bundle of Q and hence on the ordinary symplectic Poisson algebra of smooth functions on T∗Q, and the Poisson algebra of G-invariant functions on T∗Q yields a Poisson structure on the space (T∗Q) / G of G-orbits. We develop a...
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This article concerns cotangent-lifted Lie group actions; our goal is to find local and “semi-global” normal forms for these and associated structures. Our main result is a constructive cotangent bundle slice theorem that extends the Hamiltonian slice theorem of Marle [C.-M. Marle, Modèle d’action hamiltonienne d’un groupe de Lie sur une variété symplectique, Rendiconti del Seminario Matematico...
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We construct some lift of an almost complex structure to the cotangent bundle, using a connection on the base manifold. This unifies the complete lift defined by I.Satô and the horizontal lift introduced by S.Ishihara and K.Yano. We study some geometric properties of this lift and its compatibility with symplectic forms on the cotangent bundle.
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ژورنال
عنوان ژورنال: Physica D: Nonlinear Phenomena
سال: 2014
ISSN: 0167-2789
DOI: 10.1016/j.physd.2013.10.007