AIP Advances (Jun 2013)

Degeneration of the Julia set to singular loci of algebraic curves

  • Satoru Saito,
  • Noriko Saitoh,
  • Hiromitsu Harada,
  • Tsukasa Yumibayashi,
  • Yuki Wakimoto

DOI
https://doi.org/10.1063/1.4809745
Journal volume & issue
Vol. 3, no. 6
pp. 062103 – 062103

Abstract

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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.