On dynamical system relating to quantum Markov chain associated with Ising Model on Cayley tree - Mukhamedov, Farrukh; Saburov, Mansoor (INSI Publications, 2011)
In the present paper, we study stability of the dynamical system corresponding quantum Markov chain (QMC) associated with the Ising model on Cayley tree of order two. To study certain properties of QMC we reduce our investigation to the study of dynamics of a nonlinear dynamical system. For such a dynamical system it is proved existence of exactly three fixed points and absence of periodic points. Moreover, it is established finiteness and infiniteness of the trajectory of the system.