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Memoirs of the American Mathematical Society
2001; 112 pp; softcover
List Price: US$57
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Order Code: MEMO/153/727
The perturbation theory of non-commutatively integrable systems is revisited from the point of view of non-Abelian symmetry groups. Using a coordinate system intrinsic to the geometry of the symmetry, we generalize and geometrize well-known estimates of Nekhoroshev (1977), in a class of systems having almost \(G\)-invariant Hamiltonians. These estimates are shown to have a natural interpretation in terms of momentum maps and co-adjoint orbits. The geometric framework adopted is described explicitly in examples, including the Euler-Poinsot rigid body.
Graduate students and research mathematicians interested in topology and algebraic geometry.
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