| 刘维尔底频的解析拟周期三维斜对称线性系统的可约性* |
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| 引用本文： | 魏慧娟,单远,王婧. 刘维尔底频的解析拟周期三维斜对称线性系统的可约性*[J]. 数学年刊A辑(中文版), 2023, 44(3): 267-284 |
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| 作者姓名： | 魏慧娟 单远 王婧 |
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| 作者单位： | 南京理工大学数学与统计学院, 南京 210094.;南京审计大学数学学院, 南京 210029. |
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| 基金项目： | 国家重点研发计划项目(No.2021YFA1001600), 国家自然科学基金(No.11971233),江苏省自然科学基金项目(No.BK20200074)和青蓝工程项目的资助. |
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| 摘 要： | 文章主要研究一类具有刘维尔底频的解析拟周期三维斜对称线性系统的可约性.作者构造了一类三维刘维尔频率(含超刘维尔频率), 证明了在一定的非退化条件下,当扰动足够小时该类底频系统的正测旋转可约性.
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| 关 键 词： | 可约性 拟周期 刘维尔 斜对称 |
| 收稿时间： | 2022-09-18 |
| 修稿时间： | 2023-04-17 |
Reducibility of Analytic Quasi-periodic Three-Dimensional Skew Symmetric Linear Systems with Liouvillean Base Frequencies |
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| WEI Huijuan,SHAN Yuan,WANG Jing. Reducibility of Analytic Quasi-periodic Three-Dimensional Skew Symmetric Linear Systems with Liouvillean Base Frequencies[J]. Chinese Annals of Mathematics, 2023, 44(3): 267-284 |
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| Authors: | WEI Huijuan SHAN Yuan WANG Jing |
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| Affiliation: | School of Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing 210094, China.;Corresponding author. School of Mathematics, Nanjing Audit University, Nanjing 210029, China. |
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| Abstract: | In this paper, the authors mainly consider the reducibility of the analytic quasiperiodic three-dimensional skew symmetric linear systems with a class of Liouvillean base frequencies. The authors construct a class of three-dimensional Liouvillean frequencies (including super-Liouvillean frequencies), and the authors prove that under certain nonresonant conditions the system with this kind of base frequencies is rotational reducible with positive Lebesgue measure, provided that the perturbation is small enough. |
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| Keywords: | Reducibility Quasi-periodic Liouvillean Skew symmetric |
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