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Some aspects of finite-dimensional Hamiltonian dynamics

  • D. V. Treschev
Part of the NATO Science for Peace and Security Series book series (NAPSB)

These lectures touch upon two aspects of Hamiltonian mechanics. The first one (geometric) establishes fundamental role of symplectic geometry as the language of Hamiltonian mechanics. The second aspect (dynamical) exhibits the main problem in the domain, which is the interplay between regular and chaotic motion.

Keywords

Hamiltonian System Poisson Bracket Symplectic Manifold Symplectic Structure Hamiltonian Dynamic 
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References

  1. 1.
    Abraham, R, Marsden, J. Foundations of mechanics. Benjamin/Cummings Publishing Co., Inc., Advanced Book Program, Reading, MA, 1978.zbMATHGoogle Scholar
  2. 2.
    Arnold, V. I. Mathematical methods of classical mechanics. Graduate Texts in Mathematics, 60. Springer, New York, 1989.Google Scholar
  3. 3.
    Arnold, V. I., Kozlov, V. V., Neishtadt, A. I. Mathematical aspects of classical and celestial mechanics. Encyclopaedia Math. Sci., 3, Springer, Berlin, 1993. Springer, Berlin, 1997.Google Scholar

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© Springer Science + Business Media B.V 2008

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  • D. V. Treschev

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