Abstract and Applied Analysis

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

Jia Li and Junxiang Xu

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Abstract

We consider the following real two-dimensional nonlinear analytic quasi-periodic Hamiltonian system x ˙ = J x H , where H ( x , t , ϵ ) = ( 1 / 2 ) β ( x 1 2 + x 2 2 ) + F ( x , t , ϵ ) with β 0 , x F ( 0 , t , ϵ ) = O ( ϵ ) and x x F ( 0 , t , ϵ ) = O ( ϵ ) as ϵ 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.

Article information

Source
Abstr. Appl. Anal., Volume 2011, Number 1 (2011), Article ID 354063, 17 pages.

Dates
First available in Project Euclid: 15 March 2012

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1331818381

Digital Object Identifier
doi:10.1155/2011/354063

Mathematical Reviews number (MathSciNet)
MR2819767

Zentralblatt MATH identifier
1222.37049

Citation

Li, Jia; Xu, Junxiang. On the Reducibility for a Class of Quasi-Periodic Hamiltonian Systems with Small Perturbation Parameter. Abstr. Appl. Anal. 2011 (2011), no. 1, Article ID 354063, 17 pages. doi:10.1155/2011/354063. https://projecteuclid.org/euclid.aaa/1331818381


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