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Titlebook: Global Aspects of Classical Integrable Systems; Richard H. Cushman,Larry M. Bates Book 2015Latest edition Springer Basel 2015 algebra.clas

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楼主: deferential
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Ehresmann connectionsly lifted to a horizontal curve in .. An Ehresmann connection is good if every smooth curve in . has a global horizontal lift. For good connections we define the notions of parallel translation and holonomy.
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Wilfried Echterhoff,Detlev PoweleitPhysically, the . in the plane is described by a particle of unit mass acted upon by two linear springs of unit spring constant: one spring acts in the ..-direction and the other in the ..-direction. Mathematically, the . of the harmonic oscillator is Euclidean 2-space.
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In this chapter we discuss Hamiltonian systems with symmetry. By a symmetry of a Hamiltonian system (H, ., .) we mean a proper action of a Lie group G on a symplectic manifold (., .), which has a momentum mapping .: . → g*, and preserves the Hamiltonian ..
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https://doi.org/10.1057/9780230358874Here we prove the existence of local action angle coordinates for a Liouville integrable Hamiltonian system near a compact connected fiber of its integral mapping.
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The harmonic oscillatorPhysically, the . in the plane is described by a particle of unit mass acted upon by two linear springs of unit spring constant: one spring acts in the ..-direction and the other in the ..-direction. Mathematically, the . of the harmonic oscillator is Euclidean 2-space.
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