Computational Complex Dynamics of f_{α, β, γ, δ}(z)=(αz + β)/(γz² +δz)

2016/02/29 by Hassan, Sk. Sarif
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1603.00007

Abstract

The dynamics of the family of maps f_{α, β, γ, δ}(z)=(αz + β)/(γz² +δz) in complex plane is investigated computationally. This dynamical system z_n+1=f_{α, β, γ, δ}(z_n)=(αz_n + β)/(γz_n² +δz_n) has periodic solutions with higher periods which was absent in the real line scenario. It is also found that there are chaotic fractal and non-fractal like solutions of the dynamical systems. A few special cases of parameters are also have been taken care.

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