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Hamiltonian Systems

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A Course in Mathematical Physics 1

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Abstract

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

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Bibliography

  • R. Barrar. Convergence of the von Zeipel Procedure. Celestial Mechanics 2, 494–504, 1970.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • N. Bogoliubov and N. Krylov. Introduction to Non-linear Mechanics. Princeton: Princeton University Press, 1959.

    Google Scholar 

  • 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 

  • G. Giacaglia. Perturbation Methods in Non-linear Systems. New York: Springer-Verlag, 1972.

    Book  MATH  Google Scholar 

  • M. Golubitsky and V. Guillemin. Stable Mappings and their Singularities. New York: Springer-Verlag, 1973.

    Book  MATH  Google Scholar 

  • V. Guillemin and S. Sternberg. Geometric Asymptotics. Providence: American Mathematical Society, 1977.

    MATH  Google Scholar 

  • M. Hirsch and S. Smale. Differential Equations, Dynamical Systems, and Linear Algebra. New York: Academic Press, 1974.

    MATH  Google Scholar 

  • 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 

  • R. Jost. Poisson Brackets (An Unpedagogical Lecture). Rev. Mod. Phys. 36, 572–579, 1964.

    Article  ADS  Google Scholar 

  • G. Mackey. The Mathematical Foundations of Quantum Mechanics. New York: Benjamin, 1963.

    MATH  Google Scholar 

  • J. Moser, ed. Dynamical Systems: Theory and Applications. New York: Springer-Verlag, 1975.

    MATH  Google Scholar 

  • J.-M. Souriau. Structure des Systèmes Dynamiques: Maîtrises de Mathématiques. Paris: Dunod, 1970.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Institute for Theoretical Physics, University of Vienna, Austria

    Dr. Walter Thirring

  2. Massachusetts Institute of Technology, Cambridge, Massachusetts, USA

    Dr. Evans Harrell

Authors
  1. Dr. Walter Thirring
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  2. Dr. Evans Harrell
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© 1978 Springer-Verlag New York Inc.

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Thirring, W., Harrell, E. (1978). Hamiltonian Systems. In: A Course in Mathematical Physics 1. Springer, Vienna. https://doi.org/10.1007/978-3-7091-8526-1_3

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  • DOI: https://doi.org/10.1007/978-3-7091-8526-1_3

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-7091-8528-5

  • Online ISBN: 978-3-7091-8526-1

  • eBook Packages: Springer Book Archive

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