Domain of Attraction for Maps Tangent to the Identity in C2 with Characteristic Direction of Higher Degree

Sara Lapan*

*Corresponding author for this work

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

We study holomorphic fixed point germs in two complex variables that are tangent to the identity and have a degenerate characteristic direction. We show that if that characteristic direction is also a characteristic direction for higher degree terms, is non-degenerate for a higher degree term, and satisfies some additional properties, then there is a domain of attraction on which points converge to the origin along that direction.

Original languageEnglish (US)
Pages (from-to)2519-2541
Number of pages23
JournalJournal of Geometric Analysis
Volume26
Issue number4
DOIs
StatePublished - Oct 1 2016

Keywords

  • Complex dynamics
  • Domain of attraction
  • Dynamical systems
  • Holomorphic dynamics
  • Maps tangent to the identity
  • Parabolic fixed point

ASJC Scopus subject areas

  • Geometry and Topology

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