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Variational methods for the problem of Arnold diffusion

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Hamiltonian Dynamical Systems and Applications

Part of the book series: NATO Science for Peace and Security Series ((NAPSB))

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The problem of Arnold diffusion is raised for nearly integrable Hamiltonian systems. It concerns whether there exists an orbit along which the action undergoes substantial variation. Variational method has been shown a powerful tool for the study of Arnold diffusion of Hamiltonian systems convex in actions. In variational language, it amounts to construct an orbit connecting two different Aubry sets. This is the main content of the lecture notes.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Nanjing University, 210093, Nanjing, China

    Chong-Qing Cheng

Authors
  1. Chong-Qing Cheng
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Editors and Affiliations

  1. McMaster University, L8S 4K1, Hamilton, ON, Canada

    Walter Craig

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Cheng, CQ. (2008). Variational methods for the problem of Arnold diffusion. In: Craig, W. (eds) Hamiltonian Dynamical Systems and Applications. NATO Science for Peace and Security Series. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-6964-2_14

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