A Geometric Setting for Hamiltonian Perturbation Theory

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  • A Geometric Setting for Hamiltonian Perturbation Theory Book Detail

  • Author : Anthony D. Blaom
  • Release Date : 2001
  • Publisher : American Mathematical Soc.
  • Genre : Mathematics
  • Pages : 137
  • ISBN 13 : 0821827200
  • File Size : 98,98 MB

A Geometric Setting for Hamiltonian Perturbation Theory by Anthony D. Blaom PDF Summary

Book Description: 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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