Qualitative theory of p-adic dynamical systems

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• 作者：E. I. Zelenov (1)
  
• 关键词：p ; adic dynamical system ; ergodicity ; mixing ; p ; adic baker’s transformation
• 刊名：Theoretical and Mathematical Physics
• 出版年：2014
• 出版时间：February 2014
• 年：2014
• 卷：178
• 期：2
• 页码：194-201
• 全文大小：365 KB
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• 作者单位：E. I. Zelenov (1)
  
  1. Steklov Mathematical Institute, RAS, Moscow, Russia
  
• ISSN：1573-9333

文摘

We consider a class of dynamical systems over the p-adic number field: hierarchical dynamical systems. We prove a strong variant of the Poincaré theorem on the number of returns for such systems and show that hierarchical systems do not admit mixing. We describe hierarchical dynamical systems over the projective line and present an example of a nonhierarchical p-adic system that admits mixing: the p-adic baker’s transformation.