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, issue 1

Abstract: We consider the following real two‐dimensional nonlinear analytic quasi‐periodic Hamiltonian system x˙=J∇xH, where H(x,t,ε)=(12/)β(x12+x22)+F(x,t,ε) with β ≠ 0, ∂xF(0, t, ε) = O(ε) and ∂xxF(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.

Date: 2011
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https://doi.org/10.1155/2011/354063

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2011:y:2011:i:1:n:354063

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