Normal families: New perspectives

Lawrence Zalcman

Research output: Contribution to journalReview articlepeer-review

289 Scopus citations

Abstract

This paper surveys some surprising applications of a lemma characterizing normal families of merornorphic functions on plane domains. These include short and efficient proofs of generalizations of (i) the Picard Theorems, (ii) Gol'dberg's Theorem (a meromorphic function on ℂ which is the solution of a first-order algebraic differential equation has finite order), and (iii) the Fatou-Julia Theorem (the Julia set of a rational function of degree d ≥ 2 is the closure of the repelling periodic points). We also discuss Bloch's Principle and provide simple solutions to some problems of Hayman connected with this principle.

Original languageEnglish
Pages (from-to)215-230
Number of pages16
JournalBulletin of the American Mathematical Society
Volume35
Issue number3
DOIs
StatePublished - Jul 1998

Keywords

  • Algebraic differential equations
  • Bloch's principle
  • Julia set
  • Normal families
  • Picard's theorem

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