p-adic dynamical systems for $p$-adic $λ$-models on the Cayley trees

Abstract: We review and propose to use of associated dynamical system to explore the phase transition phenomena in $p$-adic statistical mechanics setting, by means of the renormalization techniques. Main focus of the paper is the $p$-adic $\lambda$-model on the Cayley tree. We study generalized $p$-adic quasi Gibbs measures for the $\lambda$-model. These measures associate recurrence equations that determine dynamical systems for the model. A main point is to verify and confirm that the indicated predictions from a dynamical system point of view are indeed true.