On chaotic behaviour of the p-adic generalized Ising mapping and its application. Issue 9 (2nd September 2017)

• Record Type: Journal Article
• Authors: Mukhamedov, Farrukh; Akın, Hasan; Dogan, Mutlay
• Is Part Of: Journal of difference equations and applications. Volume 23:Issue 9(2017)
• Page Start: 1542
• Page End: 1561
• Publication Date: 2017-09-02
• Subjects: p-adic numbers -- p-adic dynamical system -- chaos -- periodic; 46S10 -- 82B26 -- 12J12 -- 39A70 -- 47H10 -- 60K35; Difference equations -- Periodicals; 515.625
• DOI: 10.1080/10236198.2017.1340468
• Languages: English
• ISSNs: 1023-6198

Abstract

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.