On the reducibility of 2-dimensional linear quasi-periodic systems with small parameters
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- by Junxiang Xu, Wang Kun and Zhu Min
- Proc. Amer. Math. Soc. 144 (2016), 4793-4805
- DOI: https://doi.org/10.1090/proc/13088
- Published electronically: April 13, 2016
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Abstract:
In this paper we consider a real analytic linear quasi-periodic system of 2-dimension, whose coefficient matrix depends on a small parameter $C^m$-smoothly and closes to constant. Under some non-resonance conditions about the basic frequencies and the eigenvalues of the constant matrix and without any non-degeneracy assumption with respect to the small parameter, we prove that the system is reducible for many of the sufficiently small parameters.References
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Bibliographic Information
- Junxiang Xu
- Affiliation: Department of Mathematics, Southeast University, Nanjing 210096, People’s Republic of China
- MR Author ID: 609498
- ORCID: 0000-0002-2157-8560
- Email: xujun@seu.edu.cn
- Wang Kun
- Affiliation: Department of Mathematics, Southeast University, Nanjing 210096, People’s Republic of China
- Email: wangkun880304@163.com
- Zhu Min
- Affiliation: Department of Mathematics, Nanjing Forestry University, Nanjing 210037, People’s Republic of China
- Email: zhumin@njfu.edu.cn
- Received by editor(s): July 28, 2015
- Received by editor(s) in revised form: December 21, 2015, and January 9, 2016
- Published electronically: April 13, 2016
- Additional Notes: The first author was supported by the National Natural Science Foundation of China (Grant No. 11371090)
The third author was partially supported by the National Natural Science Foundation of China (Grant. No. 11401309), the NSF of the Universities in Jiangsu Province in China (No. 13KJB110012), the start high-level personnel of scientific research funds of Nanjing Forestry University in China (No.GXL2014051) and the high level academic papers published aid funds of Nanjing Forestry University in China (No:163101613) - Communicated by: Yingfei Yi
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 4793-4805
- MSC (2010): Primary 34D10, 34D23; Secondary 34C27
- DOI: https://doi.org/10.1090/proc/13088
- MathSciNet review: 3544530