KAM Theorem of Symplectic Algorithms

Kang Feng and Mengzhao Qin ()
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Kang Feng: Institute of Computational Mathematics and Scientific/Engineering Computing
Mengzhao Qin: Institute of Computational Mathematics and Scientific/Engineering Computing

Chapter Chapter 13 in Symplectic Geometric Algorithms for Hamiltonian Systems, 2010, pp 549-580 from Springer

Abstract: 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.

Keywords: Hamiltonian System; Invariant Torus; Integrable Hamiltonian System; Invariant Curf; Positive Lebesgue Measure (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-01777-3_14

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DOI: 10.1007/978-3-642-01777-3_14

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