The uniqueness of normal forms via Lie transforms and its applications to Hamiltonian systems

Details The uniqueness of normal forms via Lie transforms and its applications to Hamiltonian systems The uniqueness of normal forms via Lie transforms and its applications to Hamiltonian systems

May 1985

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985cemec..36...89l&link_type=abstract

Celestial Mechanics (ISSN 0008-8714), vol. 36, May 1985, p. 89-104.

Mathematics

Dynamical Systems

6

Dynamical Systems, Hamiltonian Functions, Orbit Perturbation, Perturbation Theory, Uniqueness Theorem, Algorithms, Celestial Mechanics, Lie Groups, Three Body Problem

Scientific paper

A necessary and sufficient condition is given for the unique normal forms about critical elements-equilibrium points and periodic orbits. With some applications to the Birkhoff's normal form along with its generalized form by K. R. Meyer, the restricted problem of three bodies near L4, the Birkhoff's normalization procedure, and the singular perturbation, of Hamiltonian systems are discussed.

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