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arXiv · 1706.01266

On chaotic behavior of the $P$-adic generalized Ising mapping and its application

Farrukh Mukhamedov·Hasan Akin·Mutlay Dogan
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Abstract

In the present paper, by conducting research on the dynamics of the $p$-adic generalized Ising mapping corresponding to renormalization group associated with the $p$-adic Ising-Vannemenus model on a Cayley tree, we have determined the existence of the fixed points of a given function. Simultaneously, the attractors of the dynamical system have been found. We have come to a conclusion that the considered mapping is topologically conjugate to the symbolic shift which implies its chaoticity and as an application, we have established the existence of periodic $p$-adic Gibbs measures for the $p$-adic Ising-Vannemenus model.

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Farrukh Mukhamedov, Hasan Akin, Mutlay Dogan. 2017-06-05. On chaotic behavior of the $P$-adic generalized Ising mapping and its application. https://doi.org/10.1080/10236198.2017.1340468

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