On chaotic behaviour of the p-adic generalized Ising mapping and its application. Issue 9 (2nd September 2017) - Mukhamedov, Farrukh; Akın, Hasan; Dogan, Mutlay
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.