English

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

Dynamical Systems 2017-03-16 v1

Abstract

We show the existence of computable complex numbers λ\lambda for which the bifurcation locus of the one parameter complex family fb(z)=λz+bz2+z3f_{b}(z) = \lambda z + b z^{2} + z^{3} is not Turing computable.

Cite

@article{arxiv.1703.04668,
  title  = {Non computable Mandelbrot-like set for a one-parameter complex family},
  author = {Daniel Coronel and Cristobal Rojas and Michael Yampolsky},
  journal= {arXiv preprint arXiv:1703.04668},
  year   = {2017}
}
R2 v1 2026-06-22T18:45:00.722Z