Speed of Arnold diffusion for analytic Hamiltonian systems

• 成果类型: Article
• 署名作者: Zhang, Ke
• 署名单位: University of Toronto
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-011-0319-6
• 发表日期: 2011
• 页码: 255-290
• 关键词: perturbation

摘要

For a convex, real analytic, epsilon-close to integrable Hamiltonian system with n >= 5 degrees of freedom, we construct an orbit exhibiting Arnold diffusion with the diffusion time bounded by exp(C epsilon (-1/2(n-2))). This upper bound of the diffusion time almost matches the lower bound of order exp(epsilon (-1/2(n-1))) predicted by the Nekhoroshev-type stability results. Our method is based on the variational approach of Bessi and Mather, and includes a new construction on the space of frequencies.