Computational Complex Dynamics of $\displaystyle{f_{α, β, γ, δ}(z)=\frac{αz + β}{γz^2 +δz}}$

Sk. Sarif Hassan

paper

Computational Complex Dynamics of $f_{α, β, γ, δ} (z) = \frac{α z + β}{γ z ^{2} + δ z}$

arXiv:1603.00007

Abstract

The dynamics of the family of maps $f_{α, β, γ, δ} (z) = \frac{α z + β}{γ z ^{2} + δ z}$ in complex plane is investigated computationally. This dynamical system $z_{n + 1} = f_{α, β, γ, δ} (z_{n}) = \frac{α z _{n} + β}{γ z _{n}^{2} + δ z _{n}}$ 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.

Computational Complex Dynamics of fα,β,γ,δ​(z)=γz2+δzαz+β​

Abstract

Computational Complex Dynamics of $f_{α, β, γ, δ} (z) = \frac{α z + β}{γ z ^{2} + δ z}$