Qp×Qp上仿射映射的动力学性质
On Dynamics of Affine Map on Qp×Qp
DOI: 10.12677/PM.2019.94070, PDF,   
作者: 肖云鹏：上海大学理学院数学系，上海
关键词: 极小分解；仿射映射；非阿基米德域；Minimal Decomposition； Affine Map； Non-Archimedean Field
摘要: 本文研究了仿射映射TA,b（X）=AX+b在二维非阿基米德空间Qp×Qp上仿射动力学的性质。主要包括对于不同类型的A，该动力系统的极小集，轨迹闭包等。
Abstract: The dynamical structure of affine map TA,b（X）=AX+b  on Qp×Qp is described in this paper. We mainly discuss minimal sets and orbit closure.
文章引用：肖云鹏. Qp×Qp上仿射映射的动力学性质[J]. 理论数学, 2019, 9(4): 533-539. https://doi.org/10.12677/PM.2019.94070

参考文献

[1] Oselies, R. and Zieschang, H. (1975) Ergodische Eigenschaften der Automorphismen p-adischer Zahlen. Archiv der Mathe-matik, 26, 144-153.
[Google Scholar] [CrossRef] 
[2] Fan, A.H., Li, M.T., Yao, J.Y. and Zhou, D. (2007) Strict Ergodicity of Affine p-Adic Dynamical Systems on Zp. Advances in Mathematics, 214, 666-700.
[3] Fan, A.H. and Fares, Y. (2011) Minimal Subsystems of Affine Dynamics on Local Fields. Archiv der Mathematik, 96, 423.
[Google Scholar] [CrossRef] 
[4] Fan, A. and Liao, L. (2011) On Minimal Decomposition of p-Adic Polynomial Dynamical Systems. Advances in Mathematics, 228, 2116--2144.
[Google Scholar] [CrossRef] 
[5] Fan, A., Fan, S., Liao, L. and Wang, Y. (2014) On Minimal Decompo-sition of p-Adic Homographic Dynamical Systems. Advances in Mathematics, 257, 92-135.
[Google Scholar] [CrossRef] 
[6] Tahar, Z., Mohamed, K. and Knapp, M. (2010) Hensel Codes of Square Roots of p-Adic Numbers. Applicable Analysis and Discrete Mathematics, 4, 32-40.
[Google Scholar] [CrossRef] 
[7] Robert, A.M. (2000) A Course in p-Adic Analysis. Springer, New York.

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