Chaotic behavior of the P-adic Potts-Bethe mapping

Farrukh Mukhamedov; Otabek Khakimov

doi:10.3934/dcds.2018011

Article Contents

2018, Volume 38, Issue 1: 231-245. Doi: 10.3934/dcds.2018011

This issue Previous Article Single-point blow-up for a multi-component reaction-diffusion system Next Article On C^{1, β} density of metrics without invariant graphs

Chaotic behavior of the P-adic Potts-Bethe mapping

Farrukh Mukhamedov^1, , and
Otabek Khakimov^2,

1.
Department of Mathematical Sciences, College of Science, The United Arab Emirates University, P.O. Box, 15551, Al Ain Abu Dhabi, UAE
2.
Institute of Mathematics of Academy of Science of Uzbekistan, 29, Do'rmon Yo'li str., 100125, Tashkent, Uzbekistan

* Corresponding author: far75m@gmail.com
* Corresponding author: far75m@gmail.com

Received: November 30, 2016

Revised: June 30, 2017

Published: October 2017

The authors would like to thank an anonymous referee for his useful suggestions which allowed to improve the content of the paper.

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In the previous investigations of the authors the renormalization group method to p-adic models on Cayley trees has been developed. This method is closely related to the investigation of p-adic dynamical systems associated with a given model. In this paper, we study chaotic behavior of the Potts-Bethe mapping. We point out that a similar kind of result is not known in the case of real numbers (with rigorous proofs).

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Mathematics Subject Classification: Primary:37B05, 37B10;Secondary:12J12, 39A70.

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