ON OMEGA LIMITING SET OF THE ISING MAPPING OVER Q_2

Nowadays in the world, it is important to define the set of all periodic Gibbs measures for lattice systems with a finite or countable set of spin values. We notice that the studying such kind problems leads us to consider discrete dynamical systems over vector spaces. In this study, we examine the discrete-time dynamics of the Ising model over the field of p-adic numbers. It is well-established that the Ising model is relevant to the theory of Gibbs measures, and every periodic point of the mapping can be characterized as a Gibbs measure for the Ising type models. We demonstrate that the dynamics of the 2-adic Ising model are regular.