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Simple proofs of some fundamental properties of the Julia set

  • Published online: 01 June 1999

Let $f$ be a holomorphic self-map of $\mathbb{C} \backslash \{ 0 \}, \mathbb{C}$, or the extended complex plane $\overline{\mathbb{C}}$ that is neither injective nor constant. This paper gives new and elementary proofs of the well-known fact that the Julia set of $f$ is a non-empty perfect set and coincides with the closure of the set of repelling cycles of $f$. The proofs use Montel–Caratheodory's theorem but do not use results from Nevanlinna theory.

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Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
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