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

Jia Li and Junxiang Xu

Abstract and Applied Analysis, 2011, vol. 2011, 1-17

Abstract:

We consider the following real two-dimensional nonlinear analytic quasi-periodic Hamiltonian system ̇ ð ‘¥ = ð ½ âˆ‡ ð ‘¥ ð » , where ð » ( ð ‘¥ , ð ‘¡ , 𠜀 ) = ( 1 / 2 ) ð ›½ ( ð ‘¥ 2 1 + ð ‘¥ 2 2 ) + ð ¹ ( ð ‘¥ , ð ‘¡ , 𠜀 ) with ð ›½ ≠0 , 𠜕 ð ‘¥ ð ¹ ( 0 , ð ‘¡ , 𠜀 ) = ð ‘‚ ( 𠜀 ) and 𠜕 ð ‘¥ ð ‘¥ ð ¹ ( 0 , ð ‘¡ , 𠜀 ) = ð ‘‚ ( 𠜀 ) as 𠜀 → 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.

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:354063

DOI: 10.1155/2011/354063

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