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

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  • Jia Li
  • Junxiang Xu

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.

Suggested Citation

  • Jia Li & Junxiang Xu, 2011. "On the Reducibility for a Class of Quasi-Periodic Hamiltonian Systems with Small Perturbation Parameter," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-17, July.
    • Handle: RePEc:hin:jnlaaa:354063
    DOI: 10.1155/2011/354063
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