Degeneration of the Julia set to singular loci of algebraic curves

@article{Saito2013DegenerationOT,
  title={Degeneration of the Julia set to singular loci of algebraic curves},
  author={Satoru Saito and Noriko Saitoh and Hiromitsu Harada and Tsukasa Yumibayashi and Yuki Wakimoto},
  journal={arXiv: Exactly Solvable and Integrable Systems},
  year={2013}
}
We show that, when a non-integrable rational map changes to an integrable one continuously, a large part of the Julia set of the map approach indeterminate points (IDP) of the map along algebraic curves. We will see that the IDPs are singular loci of the curves. 
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