Hamiltonian Systems

  • Walter Thirring
  • Evans Harrell


A 2-form is canonically defined on the cotangent bundle of a manifold. Diffeomorphisms leaving this 2-form invariant are called canonical transformations.


Phase Space Vector Field Perturbation Theory Hamiltonian System Poisson Bracket 
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  1. R. Barrar. Convergence of the von Zeipel Procedure. Celestial Mechanics 2, 494–504, 1970.MathSciNetADSMATHCrossRefGoogle Scholar
  2. N. Bogoliubov and N. Krylov. Introduction to Non-linear Mechanics. Princeton: Princeton University Press, 1959.Google Scholar
  3. J. Ford. The Statistical Mechanics of Classical Analytic Dynamics. In: Fundamental Problems in Statistical Mechanics, vol. III, E. Cohen, ed. Amsterdam: North Holland, 1975.Google Scholar
  4. G. Giacaglia. Perturbation Methods in Non-linear Systems. New York: Springer-Verlag, 1972.MATHCrossRefGoogle Scholar
  5. M. Golubitsky and V. Guillemin. Stable Mappings and their Singularities. New York: Springer-Verlag, 1973.MATHCrossRefGoogle Scholar
  6. V. Guillemin and S. Sternberg. Geometric Asymptotics. Providence: American Mathematical Society, 1977.MATHGoogle Scholar
  7. M. Hirsch and S. Smale. Differential Equations, Dynamical Systems, and Linear Algebra. New York: Academic Press, 1974.MATHGoogle Scholar
  8. W. Hunziker. Scattering in Classical Mechanics. In: Scattering Theory in Mathematical Physics, J. A. Lavita and J. Marchand, eds. Boston: D. Reidel, 1974.Google Scholar
  9. R. Jost. Poisson Brackets (An Unpedagogical Lecture). Rev. Mod. Phys. 36, 572–579, 1964.ADSCrossRefGoogle Scholar
  10. G. Mackey. The Mathematical Foundations of Quantum Mechanics. New York: Benjamin, 1963.MATHGoogle Scholar
  11. J. Moser, ed. Dynamical Systems: Theory and Applications. New York: Springer-Verlag, 1975.MATHGoogle Scholar
  12. J.-M. Souriau. Structure des Systèmes Dynamiques: Maîtrises de Mathématiques. Paris: Dunod, 1970.Google Scholar

Copyright information

© Springer-Verlag New York Inc. 1978

Authors and Affiliations

  • Walter Thirring
    • 1
  • Evans Harrell
    • 2
  1. 1.Institute for Theoretical PhysicsUniversity of ViennaAustria
  2. 2.Massachusetts Institute of TechnologyCambridgeUSA

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