Non-landing hairs in Sierpinski curve Julia sets of transcendental entire maps

@article{Garijo2010NonlandingHI,
  title={Non-landing hairs in Sierpinski curve Julia sets of transcendental entire maps},
  author={Antonio Garijo and Xavier Jarque and M{\'o}nica Moreno Rocha},
  journal={arXiv: Dynamical Systems},
  year={2010},
  pages={135-160}
}
  • Antonio Garijo, Xavier Jarque, Mónica Moreno Rocha
  • Published 2010
  • Mathematics
  • arXiv: Dynamical Systems
  • We consider the family of transcendental entire maps given by $f_a(z)=a(z-(1-a))\exp(z+a)$ where $a$ is a complex parameter. Every map has a superattracting fixed point at $z=-a$ and an asymptotic value at $z=0$. For $a>1$ the Julia set of $f_a$ is known to be homeomorphic to the Sierpi\'nski universal curve, thus containing embedded copies of any one-dimensional plane continuum. In this paper we study subcontinua of the Julia set that can be defined in a combinatorial manner. In particular, we… CONTINUE READING

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