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

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Abstract

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 Birkohoff's normalization procedure, and the singular perturbation, of Hamiltonian systems are discussed.

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Authors and Affiliations

  1. Department of Mathematics, University of Central Florida, 32816, Orlando, FL, USA

    Jong C. Liu

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  1. Jong C. Liu
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Liu, J.C. The uniqueness of normal forms via Lie transforms and its applications to Hamiltonian systems. Celestial Mechanics 36, 89–104 (1985). https://doi.org/10.1007/BF01241045

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