论文信息 - Lie Transform Tutorial

Lie Transform Tutorial — II

This survey paper is an extension of Meyer (1990) since it contains complete proofs of the main theorems and some generalizations of Lie transform theory. However, the first part of this paper deals with the applications of Lie transforms to various perturbation problems leaving the technical proofs to the later sections.

Kenneth R. Meyer | K. Meyer

[1] M. Kummer. On resonant non linearly coupled oscillators with two equal frequencies , 1976 .

[2] Ralph Abraham,et al. Foundations Of Mechanics , 2019 .

[3] André Deprit,et al. Canonical transformations depending on a small parameter , 1969 .

[4] A. Kamel. Perturbation method in the theory of nonlinear oscillations , 1970 .

[5] K. Nomizu,et al. Foundations of Differential Geometry , 1963 .

[6] A. Weinstein. Symplectic manifolds and their lagrangian submanifolds , 1971 .

[7] I. Sigal. On the discrete spectrum of the Schrödinger operators of multiparticle systems , 1976 .

[8] L. Mirsky,et al. The Theory of Matrices , 1961, The Mathematical Gazette.

[9] Kenneth R. Meyer,et al. Normal forms for Hamiltonian systems , 1974 .

[10] K. Meyer. Normal forms for the general equilibrium , 1984 .

[11] Kenneth R. Meyer,et al. Bifurcations of relative equilibria in the N -body and Kirchhoff problems , 1988 .

[12] J. Henrard. On a perturbation theory using Lie transforms , 1970 .

[13] Gen-Ichiro Hori,et al. Theory of general perturbations with unspecified canonical variables , 1966 .

[14] R. Cushman,et al. Normal form and representation theory , 1982 .