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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Persistence of the non-twist torus in nearly integrable hamiltonian systems
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by Junxiang Xu and Jiangong You PDF
Proc. Amer. Math. Soc. 138 (2010), 2385-2395 Request permission

Abstract:

In this paper we consider analytic nearly integrable hamiltonian systems, and prove that if the frequency mapping has nonzero Brouwer topological degree at some Diophantine frequency, then the invariant torus with this frequency persists under small perturbations.
References
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Additional Information
  • Junxiang Xu
  • Affiliation: Department of Mathematics, Southeast University, Nanjing 210096, People’s Republic of China
  • Email: xujun@seu.edu.cn
  • Jiangong You
  • Affiliation: Department of Mathematics, Nanjing University, Nanjing 210093, People’s Republic of China
  • MR Author ID: 241618
  • Email: jyou@nju.edu.cn
  • Received by editor(s): February 19, 2009
  • Received by editor(s) in revised form: August 3, 2009
  • Published electronically: February 18, 2010
  • Additional Notes: The first author was supported by the National Natural Science Foundation of China (10571027)
    The second author was partially supported by the National Basic Research Program of China (973 Program, 2007CB814800) and by the NNSF of China (Grant No. 10531050)
  • Communicated by: Yingfei Yi
  • © Copyright 2010 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 138 (2010), 2385-2395
  • MSC (2010): Primary 34D10, 34D23; Secondary 34C27
  • DOI: https://doi.org/10.1090/S0002-9939-10-10151-8
  • MathSciNet review: 2607868