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KAM Theorem of Symplectic Algorithms

In: Symplectic Geometric Algorithms for Hamiltonian Systems

Author

Listed:
  • Kang Feng

    (Institute of Computational Mathematics and Scientific/Engineering Computing)

  • Mengzhao Qin

    (Institute of Computational Mathematics and Scientific/Engineering Computing)

Abstract

Numerical results have shown the overwhelming superiority of symplectic algorithms over the conventional non-symplectic systems, especially in simulating the global and structural dynamic behavior of the Hamiltonian systems. In the class of Hamiltonian systems, the most important and better-understood systems are completely integrable ones. Completely integrable systems exhibit regular dynamic behavior which corresponds to periodic and quasi-periodic motions in the phase spaces. In this chapter, we study problems as to whether and to what extent symplectic algorithms can simulate qualitatively and approximate quantitatively the periodic and quasi-periodic phase curves of integrable Hamiltonian systems.

Suggested Citation

  • Kang Feng & Mengzhao Qin, 2010. "KAM Theorem of Symplectic Algorithms," Springer Books, in: Symplectic Geometric Algorithms for Hamiltonian Systems, chapter 0, pages 549-580, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-01777-3_14
    DOI: 10.1007/978-3-642-01777-3_14
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