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Nekhoroshev and KAM Stabilities in Generalized Hamiltonian Systems

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We present some Nekhoroshev stability results for nearly integrable, generalized Hamiltonian systems, which can be odd dimensional and admit a distinct number of action and angle variables. Using a simultaneous approximation technique due to Lochak, Nekhoroshev stabilities are shown for various cases of quasi-convex generalized Hamiltonian systems along with concrete estimates on stability exponents. Discussions on KAM metric stability of generalized Hamiltonian systems are also given.

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Authors and Affiliations

  1. Department of Mathematics, Jilin University, Changchun, 130012, P. R. China

    Yong Li

  2. School of Mathematics, Georgia Institute of Technology, Atlanta, GA, 30332, USA

    Yingfei Yi

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  1. Yong Li
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Li, Y., Yi, Y. Nekhoroshev and KAM Stabilities in Generalized Hamiltonian Systems. J Dyn Diff Equat 18, 577–614 (2006). https://doi.org/10.1007/s10884-006-9025-2

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