p-Adic (3, 2)-rational dynamical systems

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• 作者：I. A. Sattarov (1)
  
  1. Namangan State University ; Namangan ; Uzbekistan
  
• 关键词：rational dynamical systems ; attractors ; Siegel disk ; complex p ; adic field
• 刊名：P-Adic Numbers, Ultrametric Analysis, and Applications
• 出版年：2015
• 出版时间：January 2015
• 年：2015
• 卷：7
• 期：1
• 页码：39-55
• 全文大小：602 KB
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• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Algebra
  Russian Library of Science
  
• 出版者：MAIK Nauka/Interperiodica distributed exclusively by Springer Science+Business Media LLC.
• ISSN：2070-0474

文摘

We investigate behavior of trajectory of a (3, 2)-rational p-adic dynamical system in complex p-adic field \(\mathbb{C}_p\) . The paper studies Siegel disks and attractors of these dynamical systems. The set of fixed points of the (3, 2)-rational function may by empty, or may consist of a single element, or of two elements. We obtained the following results. In the case of existence of two fixed points, the p-adic dynamical system has a very rich behavior: we show that Siegel disks may either coincide or be disjoint for different fixed points of the dynamical system. Besides, we find the basin of the attractor of the system. For some values of the parameters there are trajectories which go arbitrary far from the fixed points.