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On the reducibility of 2-dimensional linear quasi-periodic systems with small parameters


Authors: Junxiang Xu, Wang Kun and Zhu Min
Journal: Proc. Amer. Math. Soc. 144 (2016), 4793-4805
MSC (2010): Primary 34D10, 34D23; Secondary 34C27
DOI: https://doi.org/10.1090/proc/13088
Published electronically: April 13, 2016
MathSciNet review: 3544530
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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.


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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

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

DOI: https://doi.org/10.1090/proc/13088
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
Article copyright: © Copyright 2016 American Mathematical Society