On P-adic generalized logistic dynamical system

• Main Authors: Wan Rozali, Wan Nur Fairuz Alwani, Mukhamedov, Farrukh
• Format: Conference or Workshop Item
• Language: English
• Published: 2011
• Subjects: QA Mathematics
• Online Access: http://irep.iium.edu.my/12729/1/isasm2011_3.pdf; http://irep.iium.edu.my/12729/; http://uhsb.uthm.edu.my/isasm2011/ISASM2011%20FULL%20PAPER.pdf
• Institution: Universiti Islam Antarabangsa Malaysia

Applications of p-adic numbers in p-adic mathematical physics, quantum mechanics stimulated increasing interest in the study of p-adic dynamical system. One of the interesting p-adic dynamical system is p-adic logistic map. It is known such a mapping is chaotic. In the present paper, we consider its cubic generalization namely we study a dynamical system of the form 2 f (x)  ax(1 x ) . The paper is devoted to the investigation of trajectory of the given system. We investigate the generalized logistic dynamical system with respect to parameter a. For the value of parameter, we consider the case when |a|p < 1. In this case, we study the existence of the fixed points and periodic points for every prime number, p. Not only that, their behavior also being investigated whether such fixed points and periodic points are attracting, repelling or neutral. Moreover, we describe the Siegel discs of the system, since the structure of the orbits of the system is related to the geometry of the p-adic Siegel discs.