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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Persistence of the non-twist torus in nearly integrable hamiltonian systems


Authors: Junxiang Xu and Jiangong You
Journal: Proc. Amer. Math. Soc. 138 (2010), 2385-2395
MSC (2010): Primary 34D10, 34D23; Secondary 34C27
Published electronically: February 18, 2010
MathSciNet review: 2607868
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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.


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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
Email: jyou@nju.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-10-10151-8
PII: S 0002-9939(10)10151-8
Keywords: Hamiltonian system, KAM iteration, invariant tori, non-degeneracy condition
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
Article copyright: © Copyright 2010 American Mathematical Society