Mathematics – Dynamical Systems
Scientific paper
May 1993
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993cemda..56..177m&link_type=abstract
Celestial Mechanics and Dynamical Astronomy (ISSN 0923-2958), vol. 56, no. 1-2, p. 177-190.
Mathematics
Dynamical Systems
Celestial Mechanics, Dynamical Systems, Hamiltonian Functions, Perturbation Theory, Algorithms, Kolmogorov Theory, Pendulums, Poincare Problem
Scientific paper
General properties of dynamical systems and their relationship to practical perturbation methods are reviewed focusing on a technique of successive elimination (Delaunay, 1867). The theoretical implications of the method of successive elimination of harmonics are outlined to relate the KAM approach, the Nekhoroshev theorem, and the computational algorithm. It is concluded that Delaunay's method makes it possible to clarify the relationship between the general properties of dynamical systems, as described by the KAM and Nekhoroshev approaches, and the computational algorithm for the effective analysis of specific systems.
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