Inclusions of invariant subalgebras S(g)^G subset S(g)^T subset S(g) for a maximal torus T in a semisimple Lie group G form a superintegrable Poisson projection chain with matching dimension splits between Hamiltonians and integrals.
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Constructs two commuting families of polynomial first integrals for magnetic geodesic flows on reductive homogeneous spaces G/A, yielding a superintegrable system via a reduced Poisson algebra in a dense regular locus.
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Geometric construction of superintegrable Poisson projection chains via Poisson centralizers
Inclusions of invariant subalgebras S(g)^G subset S(g)^T subset S(g) for a maximal torus T in a semisimple Lie group G form a superintegrable Poisson projection chain with matching dimension splits between Hamiltonians and integrals.
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Poisson Centralisers and Polynomial Superintegrability for Magnetic Geodesic Flows on Reductive Homogeneous Spaces
Constructs two commuting families of polynomial first integrals for magnetic geodesic flows on reductive homogeneous spaces G/A, yielding a superintegrable system via a reduced Poisson algebra in a dense regular locus.