Dynamical systems with homogeneous configuration spaces
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All G-invariant Hamiltonian systems on T*(G/K) are integrable within the class of Noether integrals.
The subgroup K of G is spherical; i.e., the quasiregular representation of G on the space C[G/K] of regular functions on the affine algebraic variety G/K has a simple spectrum if G is complex, and likewise on L 2(G/K) if G is compact. In (Guillemin et al, 1984a) it was shown that a subgroup K of a compact Lie group G is spherical if and only if
The algebra of G-invariant functions on T*(G/K) is commutative with respect to the standard Poisson bracket.
KeywordsPoisson Bracket Poisson Structure Borel Subalgebra Zariski Open Subset Hamiltonian Vector Field
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