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Normal Form for Families of Hamiltonian Systems

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Abstract

We consider perturbations of integrable Hamiltonian systems in the neighborhood of normally parabolic invariant tori. Using the techniques of KAM-theory we prove that there exists a canonical transformation that puts the Hamiltonian in normal form up to a remainder of weighted order 2d + 1. And some dynamical consequences are obtained.

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Authors and Affiliations

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

    Zhi Guo Wang

  2. School of Mathematical Sciences, Suzhou University, Suzhou 215006, P. R. China

    Zhi Guo Wang

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  1. Zhi Guo Wang
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Correspondence to Zhi Guo Wang.

Additional information

The work is supported by the National Natural Science Foundation of China (19925107) and the Special Funds for Major State Basic Research Projects of China (973 Projects)

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Wang, Z.G. Normal Form for Families of Hamiltonian Systems. Acta Math Sinica 23, 1199–1216 (2007). https://doi.org/10.1007/s10114-005-0844-6

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  • DOI: https://doi.org/10.1007/s10114-005-0844-6

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