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TMF, 2014, Volume 178, Number 2, Pages 220–229 (Mi tmf8543)  

Qualitative theory of $p$-adic dynamical systems

E. I. Zelenov

Steklov Mathematical Institute, RAS, Moscow, Russia

Abstract: 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.

Keywords: $p$-adic dynamical system, ergodicity, mixing, $p$-adic baker's transformation

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation НШ-2928.2012.1
Russian Foundation for Basic Research 11-01-00828_a
11-01-12114-oфи_м


DOI: https://doi.org/10.4213/tmf8543

Full text: PDF file (378 kB)
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English version:
Theoretical and Mathematical Physics, 2014, 178:2, 194–201

Bibliographic databases:

Document Type: Article
Received: 21.04.2013

Citation: E. I. Zelenov, “Qualitative theory of $p$-adic dynamical systems”, TMF, 178:2 (2014), 220–229; Theoret. and Math. Phys., 178:2 (2014), 194–201

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