Attracting domains of maps tangent to the identity whose only characteristic direction is non-degenerate

Sara W. Lapan*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

Let f be a holomorphic germ on ℂ2 that fixes the origin and is tangent to the identity. Assume that f has a non-degenerate characteristic direction [v]. Hakim gave conditions that guarantee the existence of attracting domains along [v], however, when f has only one characteristic direction, these conditions are not satisfied. We prove that when [v] is unique, the existence results still hold. In particular, there is a domain Ω whose points converge to the origin along [v] and, on Ω, f is conjugate to a translation. Furthermore, if f is a global automorphism, the corresponding domain of attraction is a Fatou-Bieberbach domain.

Original languageEnglish (US)
Article number1350083
JournalInternational Journal of Mathematics
Volume24
Issue number10
DOIs
StatePublished - Sep 2013

Keywords

  • Fatou-Bieberbach domains
  • Holomorphic dynamics
  • domains of attraction
  • tangent to the identity

ASJC Scopus subject areas

  • Mathematics(all)

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