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Reducibility of slow quasi-periodic linear systems


Authors: Jian Wu and Jiangong You
Journal: Proc. Amer. Math. Soc. 141 (2013), 3147-3155
MSC (2010): Primary 37C05, 37C15, 37J40, 34A30, 34C27
DOI: https://doi.org/10.1090/S0002-9939-2013-11915-5
Published electronically: May 21, 2013
MathSciNet review: 3068968
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Abstract: In this note, we prove that the reducibility of analytic quasi-periodic linear systems close to constant is irrelevant to the size of the base frequencies. More precisely, we consider the quasi-periodic linear systems

$\displaystyle \dot {X} =(A+B(\theta ))X,\quad \dot {\theta }=\lambda ^{-1}\omega $

in $ \mathbb{C}^{m},$ where the matrix $ A$ is constant and $ \omega $ is a fixed Diophantine vector, $ \lambda \in \mathbb{R}\backslash \{0\}$. We prove that the system is reducible for typical $ A$ if $ B(\theta )$ is analytic and sufficiently small (depending on $ A, \omega $ but not on $ \lambda $).

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Additional Information

Jian Wu
Affiliation: Department of Mathematics, Nanjing University, Nanjing 210093, People’s Republic of China
Email: wujian0987@gmail.com

Jiangong You
Affiliation: Department of Mathematics, Nanjing University, Nanjing 210093, People’s Republic of China
Email: jyou@nju.edu.cn

DOI: https://doi.org/10.1090/S0002-9939-2013-11915-5
Keywords: Reducibility, slow quasi-periodic linear systems
Received by editor(s): March 24, 2011
Received by editor(s) in revised form: November 23, 2011
Published electronically: May 21, 2013
Additional Notes: This work is partially supported by the NSF of China, grant no. 11031003. This work is also partially supported by Scientific Research and Innovation Project for College Postgraduates in Jiangsu, China (CXZZ120029), and a project funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions
Communicated by: Walter Craig
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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