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A geometric setting for Hamiltonian perturbation theory

About this Title

Anthony D. Blaom

Publication: Memoirs of the American Mathematical Society
Publication Year 2001: Volume 153, Number 727
ISBNs: 978-0-8218-2720-8 (print); 978-1-4704-0320-1 (online)
MathSciNet review: 1848237
MSC: Primary 37J40; Secondary 37J15, 70G45, 70H06, 70H08, 70H09, 70H33

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Table of Contents


  • Introduction
  • Part 1. Dynamics
  • 1. Lie-theoretic preliminaries
  • 2. Action-group coordinates
  • 3. On the existence of action-group coordinates
  • 4. Naive averaging
  • 5. An abstract formulation of Nekhoroshev’s theorem
  • 6. Applying the abstract Nekhoroshev theorem to action-group coordinates
  • 7. Nekhoroshev-type estimates for momentum maps
  • Part 2. Geometry
  • 8. On Hamiltonian $G$-spaces with regular momenta
  • 9. Action-group coordinates as a symplectic cross-section
  • 10. Constructing action-group coordinates
  • 11. The axisymmetric Euler-Poinsot rigid body
  • 12. Passing from dynamic integrability to geometric integrability
  • 13. Concluding remarks