Non computable Mandelbrot-like set for a one-parameter complex family

14 Mar 2017 · Coronel Daniel, Rojas Cristobal, Yampolsky Michael ·

We show the existence of computable complex numbers $\lambda$ for which the bifurcation locus of the one parameter complex family $f_{b}(z) = \lambda z + b z^{2} + z^{3}$ is not Turing computable.