A Geometric Setting For Hamiltonian Jperturbation Theory
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A Geometric Setting for Hamiltonian Perturbation Theory
Author | : Anthony D. Blaom |
Publisher | : American Mathematical Soc. |
Total Pages | : 137 |
Release | : 2001 |
Genre | : Mathematics |
ISBN | : 0821827200 |
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In this text, the perturbation theory of non-commutatively integrable systems is revisited from the point of view of non-Abelian symmetry groups. Using a co-ordinate system intrinsic to the geometry of the symmetry, the book generalizes and geometrizes 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.
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