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Answers
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5
Splitting of the double tangent bundle into vertical and horizontal parts, and defining partial derivatives
5
A $C^2$ small autonomous Hamiltonian has only constant 1-periodic orbits
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Books you would like to read (if somebody would just write them…)
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Why does the group act on the right on the principal bundle?
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Book on Symplectic Geometry
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When is a symplectic manifold equivalent to a cotangent bundle?