On a p-adic cubic generalized logistic dynamical system

Applications of p-adic numbers mathematical physics, quantum mechanics stimulated increasing interest in the study of p-adic dynamical system. One of the interesting investigations is p-adic logistics map. In this paper, we consider a new generalization, namely we study a dynamical system of the form f_a(x) ax(1-x²). The paper is devoted to the investigation of a trajectory of the given system. We investigate the generalized logistic dynamical system with respect to parameter a and we restrict ourselves for the investigation of the case |a|_p < 1. We study the existence of the fixed points and their behavior. Moreover, we describe their size of attractors and Siegel discs since the structure of the orbits of the system is related to the geometry of the p-adic Siegel discs.