scholarly journals Normalization of the periodic Hamiltonian system

2019 ◽  
pp. 1-18 ◽  
Author(s):  
Alexander Dmitrievich Bruno
Keyword(s):  
Hamiltonian System ◽  
Periodic Hamiltonian System

scholarly journals On the Reducibility for a Class of Quasi-Periodic Hamiltonian Systems with Small Perturbation Parameter

2011 ◽  
Vol 2011 ◽  
pp. 1-17 ◽  
Author(s):  
Jia Li ◽  
Junxiang Xu
Keyword(s):  
Hamiltonian System ◽  
Hamiltonian Systems ◽  
Small Perturbation ◽  
Perturbation Parameter ◽  
Nondegeneracy Condition ◽  
Two Dimensional ◽  
Symplectic Transformation ◽  
Periodic Hamiltonian System

We consider the following real two-dimensional nonlinear analytic quasi-periodic Hamiltonian systemx˙=J∇xH, whereH(x,t,ε)=(1/2)β(x12+x22)+F(x,t,ε)withβ≠0,∂xF(0,t,ε)=O(ε)and∂xxF(0,t,ε)=O(ε)asε→0. Without any nondegeneracy condition with respect to ε, we prove that for most of the sufficiently small ε, by a quasi-periodic symplectic transformation, it can be reduced to a quasi-periodic Hamiltonian system with an equilibrium.

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